Answer:
95% Confidence interval: (39.43, 61.58)
Step-by-step explanation:
We are given the following in the question:
Sample mean, [tex]\bar{x}[/tex] = $50.50
Sample size, n = 15
Alpha, α = 0.05
Sample standard deviation = 20
95% Confidence interval:
[tex]\bar{x} \pm t_{critical}\displaystyle\frac{s}{\sqrt{n}}[/tex]
Putting the values, we get,
[tex]t_{critical}\text{ at degree of freedom 14 and}~\alpha_{0.05} = \pm 2.1447[/tex]
[tex]=50.50 \pm 2.1447(\dfrac{20}{\sqrt{15}} ) \\\\= 50.50 \pm 11.0751 \\= (39.4249,61.5751)\\\approx (39.43, 61.58)[/tex]
95% Confidence interval: (39.43, 61.58)
The 95% confidence interval for the mean amount spent on their first visit to the chain's new store in the mall by credit card customers is approximately $41.99 to $59.01.
Explanation:We can construct the 95% confidence interval using the sample mean ( X = $50.50) and the standard deviation ( S = $20). Since we know that the distribution is normal, we can use the z-score for a 95% confidence level, which is approximately 1.96.
The formula for a confidence interval is given by: X ± Z*(S/√n). By substituting the given values into the formula, we get: 50.5 ± 1.96*(20/√15).
After calculating, we find that the 95% confidence interval is approximately $41.99 - $59.01. Thus, we are 95% confident that the true mean amount spent by the department store's credit card customers on their first visit is between $41.99 and $59.01.
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A restaurant purchased kitchen equipment on January 1, 2017. On January 1, 2019, the value of the equipment was $14 comma 550. The value after that date was modeled as follows. V(t)equals 14 comma 550 e Superscript negative 0.158 t a) What is the rate of change in the value of the equipment on January 1, 2019
Answer:
[tex]\frac{dV(t)}{dt} =[/tex] - 1675.38
Step-by-step explanation:
In 2017, the vakue of the kitchen equipment was $14550
V(0)=$14550
Its value after then was modelled by [tex]V(t)=14550e^{-0.158t[/tex]
We are required to find the rate of change in value on January 1, 2019
[tex]V(t)=14550e^{-0.158t[/tex]
[tex]\frac{dV(t)}{dt} =\frac{d}{dt}14550e^{-0.158t[/tex]
[tex]\frac{dV(t)}{dt} =14550 \frac{d}{dt}e^{-0.158t[/tex]
[tex]\\Let u= -0.158t,\frac{du}{dt}=-0.158[/tex]
[tex]\frac{dV(t)}{dt} =14550 \frac{d}{du}e^u\frac{du}{dt}[/tex]
[tex]\frac{dV(t)}{dt} =14550 X -0.158 e^{-0.158t}=-2298.9e^{-0.158t}[/tex]
In 2019, i.e. 2 years after, t=2
The rate of change of the value
[tex]\frac{dV(t)}{dt} =-2298.9e^{-0.158X2}[/tex]
=[tex]\frac{dV(t)}{dt} =-2298.9e^{-0.316}[/tex]= - 1675.38
The rate of change in the value of the equipment on January 1, 2019, is -2,302.9e^(-0.158t).
Explanation:The rate of change in the value of the equipment on January 1, 2019, can be found by taking the derivative of the given model equation V(t) = 14,550e^(-0.158t).
The derivative of V(t) with respect to t is dV/dt = -0.158(14,550)e^(-0.158t), which simplifies to dV/dt = -2,302.9e^(-0.158t).
Therefore, the rate of change in the value of the equipment on January 1, 2019, is -2,302.9e^(-0.158t).
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(1 point) Suppose we will flip a fair coin 100 times. (a) What does 35 heads correspond to on the standard scale? (enter exact answer) (b) What does z=2.4 on the standard scale correspond to on the number of heads scale? (enter exact answer)
Answer:
(a) 35 heads correspond to -3 on the standard scale.
(b) z = 2.4 corresponds to 62 heads on the number of heads scale.
Step-by-step explanation:
(a) If we flip a fair coin once, probability of getting head = 0.5
If we flip a fair coin 100 times, mean number of heads = 100(0.5) = 50
If there are N draws with a P probability of success, the standard deviation (SD) is given as:
[tex]SD = \sqrt{(N)(P)(1 - P)}[/tex]
Here, the probability of getting a head (P) is 0.5 while the number of draws (N) is 100. So,
[tex]SD = \sqrt{(100)(0.5)(1-0.5)}[/tex]
SD = 5
The standard scale value is: (35 - 50) / 5 = -3
Hence, 35 heads correspond to -3 on the standard scale.
(b) The standard scale value is 2.4 and we need to find the number of heads.
(X - 50) / 5 = 2.4
X - 50 = 12
X = 62
Hence, z = 2.4 on the standard scale corresponds to 62 on the number of heads scale.
The 35 heads corresponds to -3 on the standard scale, and the number of heads is 62
The head on the standard scale
The given parameter is:
n = 100
In a flip of a coin, the probability of a head is:
p = 1/2
So, the mean of the distribution is:
[tex]\bar x = np[/tex]
[tex]\bar x = 100 * 1/2[/tex]
[tex]\bar x = 50[/tex]
The standard deviation is:
[tex]\sigma = \sqrt{np(1 - p)}[/tex]
So, we have:
[tex]\sigma = \sqrt{100 * 1/2 * (1 - 1/2)}[/tex]
[tex]\sigma = 5[/tex]
The corresponding value on the standard scale is then calculated as:
[tex]z= \frac{x - \mu}{\sigma}[/tex]
For 35 heads, we have:
[tex]z= \frac{35 - 50}{5}[/tex]
[tex]z = -3[/tex]
Hence, the 35 heads corresponds to -3 on the standard scale
(b) The number of heads
We have:
[tex]z= \frac{x - \mu}{\sigma}[/tex]
When z = 2.4, the equation becomes
[tex]2.4= \frac{x - 50}{5}[/tex]
Multiply both sides by 5
[tex]12= x - 50[/tex]
Add 50 to both sides
[tex]x = 62[/tex]
Hence, the number of heads is 62
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The temperature at a point (x,y,z) is given by T(x,y,z)=200e^-x^2-3y^-9z^2, where T measured in degrees Celsius and x,y,z in meters. Find the rate of change of temperature at the point P(2, -1, 2) in the direction toward the point (3, -3, 3)
Answer:
Therefore the rate change of temperature at the point P(2,-1,2) in the direction toward the point (3,-3,3) is [tex]-\frac{5200\sqrt6}{3}e^{-43}[/tex] °C/m.
Step-by-step explanation:
Given that, the temperature at a point (x,y,z) is
[tex]T(x,y,z)=200e^{-x^2-3y^2-9z^2}[/tex].
Rate change of temperature at the point P(2,-1,2) in the direction toward the point Q (3,-3,3) is [tex]D_uT(2,-1,2)[/tex]
[tex]T_x= 200(-2x)e^{-x^2-3y^2-9z^2}[/tex][tex]=-400x200.2xe^{-x^2-3y^2-9z^2}[/tex]
[tex]T_y = 200.(-6y)e^{-x^2-3y^2-9z^2}[/tex][tex]=-1200ye^{-x^2-3y^2-9z^2}[/tex]
[tex]T_z=200(-18z)e^{-x^2-3y^2-9z^2}[/tex][tex]=-3600ze^{-x^2-3y^2-9z^2}[/tex]
The gradient of the temperature
[tex]\bigtriangledown T(x,y,z)= (-400x200.2xe^{-x^2-3y^2-9z^2},-1200ye^{-x^2-3y^2-9z^2},-3600ze^{-x^2-3y^2-9z^2})[/tex] [tex]=-400e^{-x^2-3y^2-9z^2}(x,3y,9z)[/tex]
[tex]\bigtriangledown T(2,-1,2) = -400e^{-2^2-3(-1)^2-9.2^2}(2,3.(-1),9.2)[/tex]
[tex]=-400 e^{-43}(2,-3,18)[/tex]
V=[tex]\overrightarrow {PQ}= \vec{Q}-\vec{P}[/tex]=(3,-3,3)-(2,-1,2)=(1,-2,1)
The unit vector of V is [tex]\frac{(1,-2,1)}{\sqrt{1^2+(-2)^2+1^2}}[/tex]
[tex]=\frac{1}{\sqrt6}(1,-2,1)[/tex]
Therefore,
[tex]D_uT(2,-1,2) = \bigtriangledown T(2,-1,2).\frac{1}{\sqrt6}(1,-2,1)[/tex]
[tex]=-400 e^{-43}(2,-3,18).\frac{1}{\sqrt6}(1,-2,1)[/tex]
[tex]=-\frac{400}{\sqrt6}e^{-43}(2.1+(-3).(-2)+18.1)[/tex]
[tex]=-\frac{10400}{\sqrt6}e^{-43}[/tex]
[tex]=-\frac{5200\sqrt6}{3}e^{-43}[/tex] °C/m
Therefore the rate change of temperature at the point P(2,-1,2) in the direction toward the point (3,-3,3) is [tex]-\frac{5200\sqrt6}{3}e^{-43}[/tex] °C/m.
The number of errors in a textbook follow a Poisson distribution with a mean of 0.03 errors per page. What is the probability that there are 3 or less errors in 100 pages? Round your answer to four decimal places (e.g. 98.7654).
Answer:
Therefore the required probability is 0.6472.
Step-by-step explanation:
Poisson distribution: A Poisson distribution is discrete distribution.
Let X be a discrete variable the number of event. Let λ be the mean of X.
Then the probability of k event is
[tex]P(X=k)=\frac{\lambda^ke^{-\lambda}}{k!}[/tex]
Here mean of each page is =0.03
Mean of 100 pages = (0.03×100)= 3
λ = 3
The required probability
P(X≤3)
= P(X=0)+P(X=1)+P(X=2)+P(X=3)
[tex]=\frac{3^0e^{-3}}{0!}[/tex] [tex]+\frac{3^1e^{-3}}{1!}[/tex][tex]+\frac{3^2e^{-3}}{2!}[/tex][tex]+\frac{3^3e^{-3}}{3!}[/tex]
[tex]=e^{-3}(1+3+\frac{9}{2}+\frac{27}{6})[/tex]
[tex]=e^{-3}(13)[/tex]
≈ 0.6472
Therefore the required probability is 0.6472
An ANOVA procedure is used for data obtained from four populations. Four samples, each comprised of 30 observations, were taken from the four populations. The numerator and denominator (respectively) degrees of freedom for the critical value of F are _____.
Answer:
Step-by-step explanation:
Given that an ANOVA procedure is used for data obtained from four populations. Four samples, each comprised of 30 observations, were taken from the four populations.
Hence total observations are 30*4 =120
No of groups = 3
Hence numerator df = 3-1 =2
Now total degrees of freedom = 120-1 =119
So denominator degrees of freedom = 119-2 = 117
Thus F statistic will have numerator as 2 degrees of freedom and denominator as 117 degrees of freedom.
In 1906 Kennelly developed a simple formula for predicting an upper limit on the fastest time that humans could ever run distances from 100 yards to 10 miles. His formula is given by t equals . 0588 s Superscript 1.125 where s is the distance in meters and t is the time to run that distance in seconds. a. Find Kennelly's estimate for the fastest a human could possibly run 1606 meters. tequals nothing seconds (Round to the nearest thousandth as needed.) b. Find StartFraction dt Over ds EndFraction when sequals20 and interpret your answer. StartFraction dt Over ds EndFraction almost equals nothing sec/m (Round to the nearest thousandth as needed.) When the distance is 20 meters, this rate gives the number of seconds per meter ▼ by which the fastest possible time is increasing. by which the fastest possible time is decreasing. that the fastest human could possibly run.
Answer / Step-by-step explanation:
(1) Given t = 0.0588s ¹.¹²⁵
where s is the distance and t is the time to run that distance.
The second portion asks us to find the derivative of the equation when our s value is equal to 20 and interpret.
(2) First, we try to convert the unit from miles to meters
Therefore, 1 mile = 1609 meters
Then,
t = 0.0588 ( 1609 ) ¹.¹²⁵
=238 . 09
This gives us the instantaneous rate of change of seconds between every 20 meters ran.
The last portion asks us to compare this estimate to current world records. And have they been surpassed?
As of today, the fastest official record for a standard mile is held by a man from Morocco named Hichan El Guerrouj. The time was recorded at 3.43 minutes in Rome, Italy on July 7th, 1999.
Now, keep in mind that this is almost a full minute slower than the estimated time. However, how do these projections hold up against Usain Bolt, the man that is considered the fastest man in the world ?
Although, Usain Bolt does run long distances, he holds records in nearly every sprinting event that he has ever competed in.
Hence, Kennelly's estimate for the fastest mile is 238.09
(3) Now, noting that since dt / ds = 0.0588 ( 1.25 ) s ⁰.¹²⁵
Then,
dt / ds I 100 = 0.0588 (1.25) (20) ⁰.¹²⁵
= 0.1176
Consider a with 3 × 3 grid where each cell contains a number of coins; for example, the following represents a possible configuration of coins on the grid (the integer in each cell is the number of coins in that cell):12 3 11 8 42 13 0This configuration is transformed in stages as follows: in each step, every cell sends a coin to all of its neighbors (horizontally or vertically, not diagonally), but if there aren’t enough coins in a cell to send one to each of its neighbors, it sends no coins at all. For example, the above would result in the following after one step:11 2 34 7 21 12 2a) Show that every staring configuration results in stable configuration (one that no longer changes in this process), or repeatedly cycles through ???? configurations for some positive integer ???? (i.e., those same ???? configurations appear repeatedly in the sequence over and over as the transformation is applied).b) In the case that the initial configuration eventually cycles through ???? configurations, what are the possible values of ?????c) Either prove that for some positive integer ????, every configuration will reach a stable configuration or a repetition of a ????-cycle in ???? or fewer steps, or prove there is no such B.
Answer:
Step-by-step explanation:
Check attachment for solution
To assess the opinion of students at The Ohio State University about campus safety, a reporter for the student newspaper interviews 15 students she meets walking on the campus late at night who are willing to give their opinion. If the reporter instead decided to interview every fifth student that walks by, the method of sampling would be: a. simple random sampling. b. stratified random sampling. c. systematic sampling. d. a census.
Answer:
(C) Systematic Sampling
Step-by-step explanation:
The reporter decides to interview every fifth student of Ohio State University that passes by. This is referred to as Systematic Sampling.
In Systematic Sampling, the members of the population are place in an ordered list and the members of the sample are taken at a stated interval. This interval is called the Sampling Interval.
Although the members of the sample are random, they are chosen at stated intervals.
The cost of flying a passenger plane from point A to point B is $70 comma 00070,000. The airline flies this route four times per day at 7 AM, 10 AM, 1 PM, and 4 PM. The first and last flights are filled to capacity with 240240 people. The second and third flights are only half full. Find the average cost per passenger for each flight.
Answer:
I. $291.67 per passenger
II. $583.33 per passenger
Step-by-step explanation:
The cost of flying the passenger plane from A to B is $70,000.
If the Capacity of the plane is 240 people.
(I)At 7A.M and 4P.M., the average cost per passenger is given as:
Average Cost=Total Cost/Number of Passengers
=70000/240=$291.67 per passenger
(II)At 10AM and 1PM, the flight is only half full, it has 120 passengers.
Average Cost = 70000/120=$583.33 per passenger
Answer: The cost will be $291.70 and $583.40 for the first and the last and for the second and third flights, respectively.
Step-by-step explanation: The cost is $70,000, the full capacity of seats is 240 and half capacity is 120.
In the first and last flights, which have the full capacity, the average cost per passenger is:
C = [tex]\frac{70,000}{240}[/tex] = 291.70
In the second and third ones, the average cost is:
C = [tex]\frac{70,000}{120}[/tex] = 583.4
The average cost per passenger for the first and the last flight are $291.70, while for the second and third are $583.4
In a large, randomly mating population with no forces acting to change gene frequencies, the frequency of homozygous recessive individuals for the character extra-long eyelashes is 90 per 1000, or 0.09. What percentage of the population carries this trait but displays the dominant phenotype, short eyelashes
Answer:
16.38%
Step-by-step explanation:
Given
Frequency of homozygous recessive individuals for the character extra-long eyelashes is 90 per 1000
Let p = Probability of homozygous recessive individuals having character extra-long eyelashes = 0.09
p + q = 1 where q = Probability of homozygous recessive individuals not having character extra-long eyelashes
0.09 + p = 1
p = 1 - 0.09
p = 0.91
The frequency of the carrier individual is calculated by npq
Where n = mating partners = 2
Frequency = 2 * 0.09 * 0.91
Frequency = 0.1638 or 16.38%
Answer:
The percentage of the population carries this trait but displays the dominant phenotype, short eyelashes is the frequency of hetrozygous individuals which is
0.42 or 42 %
Step-by-step explanation:
To solve the question, we note that
p²+2pq+q²=1 and p + q =1
where
p = frequency of the dominant allele
q= frequency of the recessive allele
p² = frequency of homozygous dominant allele
q² = frequency of homozygous recessive allele
2·p·q = frequency of hetrozygous individuals
The frequency of the homozygous recessive individuals q² is 0.09
Therefore the frequency of q = √(0.09) = 0.3, therefore p = 1 - 0.3 =0.7
The percentage of the population carries this trait but displays the dominant phenotype, short eyelashes is the frequency of hetrozygous individuals or 2×p×q = Ae = 2*0.3*0.7 = 0.42
→ 0.42× 100 = 42 %
What is slope of line between each pair of points?
(1, -19) and (-2, -7)
The slope of the line is [tex]m=-4[/tex]
Explanation:
Given that the pair of points are [tex](1,-19)[/tex] and [tex](-2,-7)[/tex]
We need to determine the slope of the line.
The slope of the line can be determined using the formula,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substituting the points [tex](1,-19)[/tex] and [tex](-2,-7)[/tex] for the coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] in the above formula, we have,
[tex]m=\frac{-7-(-19)}{-2-1}[/tex]
Simplifying the terms, we get,
[tex]m=\frac{-7+19}{-2-1}[/tex]
Adding the terms, we have,
[tex]m=\frac{12}{-3}[/tex]
Dividing, we get,
[tex]m=-4[/tex]
Thus, the slope of the line between the pair of points is [tex]m=-4[/tex]
please someone help me!!!! SHOW ALL WORK! ive been stuck on this question for 2 days!! :((((((
Step-by-step explanation:
x² + y² − 8x + 10y − 8 = 0
Rearrange:
x² − 8x + y² + 10y = 8
To complete the square, take half of the x and y coefficients, square it, then add the result to both sides.
(-8/2)² = 16
(10/2)² = 25
x² − 8x + 16 + y² + 10y + 25 = 8 + 16 + 25
x² − 8x + 16 + y² + 10y + 25 = 49
Factor the squares:
(x − 4)² + (y + 5)² = 49
The center is (4, -5) and the radius is 7.
In remodeling a kitchen, a builder decides to place a splash-guard behind the sink consisting of eight 6-inch-square ceramic tiles decorated with different botanical herbs. The tiles will be installed in a custom-made wooden panel. The tile supplier has 12 different herb designs to choose from, and the builder selects 8 of these 12 at random. Suppose the order in which the tiles are arranged on the splash-guard does not matter. Fill in the blanks. (Give your answers to four decimal places.)
Two of the 12 herb tiles contain a blue tint that matches the kitchen color scheme. The probability that these 2 tiles will be included in the splash-guard is __.
The family actually grows 5 of the 12 herbs in a backyard garden. The probability that all 5 of these will be included on the splash-guard is _
Answer:
(a) 0.4242
(b) 0.0707
Step-by-step explanation:
The total number of ways of selecting 8 herbs from 12 is
[tex]\binom{12}{8}=495[/tex]
(a) If 2 herbs are selected, then there are 8 - 2 = 6 herbs to be selected from 12 - 8 = 10. The number of ways of the selection is then
[tex]\binom{10}{6}= 210[/tex]
Note that this is the number of ways that both are included. We would have multiplied by 2! if any of them were to be included.
The probability = [tex]\dfrac{210}{495}=0.4242[/tex]
(b) If 5 herbs are selected, then there are 8 - 5 = 3 herbs to be selected from 12 - 5 = 7. The number of ways of the selection is then
[tex]\binom{7}{3}= 35[/tex]
This is the number of ways that both are included. We would have multiplied by 5! if any of them were to be included. In that case, our probability will exceed 1; this implies that certainly, at least, one of them is included.
The probability = [tex]\dfrac{35}{495}=0.0707[/tex]
The probability that the 2 tiles with a blue tint will be included in the splash-guard is 0.0455. The probability that all 5 of the herbs grown in the backyard garden will be included on the splash-guard is 0.0058.
The probability that the 2 tiles with a blue tint will be included in the splash-guard is 0.0455.
The probability that all 5 of the herbs grown in the backyard garden will be included on the splash-guard is 0.0058.
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Two fair six-sided dice are tossed independently. Let M 5 the maximum of the two tosses (so M(1,5) 5 5, M(3,3) 5 3, etc.). a. What is the pmf of M? [Hint: First determine p(1),
Answer with Step-by-step explanation:
S={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),..,(2,6),(3,1),(3,2),...,(3,6),(4,1),..,(4,6),(5,1),(5,2),(5,3),...,(5,6),(6,1),(6,2),..,(6,6)}
Total number of cases=36
M=Maximum of the two tosses
M=1,
(1,1)
Therefore, [tex]P(1)=\frac{1}{36}[/tex]
Using the formula, P(E)=[tex]\frac{favorable\;cases}{Total\;number\;of\;cases}[/tex]
M=2
(1,2),(2,1),(2,2)
Favorable cases=3
[tex]P(2)=\frac{3}{36}=\frac{1}{12}[/tex]
M=3
(1,3),(3,1),(3,2),(2,3),(3,3)
[tex]P(3)=\frac{5}{36}[/tex]
M=4
(1,4),(4,1),(2,4),(3,4),(4,2)(4,3),(4,4)
[tex]P(4)=\frac{7}{36}[/tex]
M=5
(1,5),(2,5),(3,5),(4,5),(5,1),(5,2),(5,3),(5,4),(5,5)
[tex]P(5)=\frac{9}{36}=\frac{1}{4}[/tex]
M=6
(1,6),(2,6),(3,6),(4,6),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)
[tex]P(6)=\frac{11}{36}[/tex]
You have one type of chocolate that sells for $2.40/lb and another type of chocolate that sells for $9.90/lb. You would like to have 30 lbs of a chocolate mixture that sells for $4.20/lb. How much of each chocolate will you need to obtain the desired mixture
Final answer:
To obtain the desired mixture, you will need 24 lbs of the first type of chocolate and 6 lbs of the second type of chocolate.
Explanation:
To find the amount of each chocolate needed to obtain the desired mixture, we can set up a system of equations. Let's say x represents the pounds of the first type of chocolate and y represents the pounds of the second type of chocolate. We know that the total weight of the mixture is 30 lbs, so we have the equation:
x + y = 30
We also know that the cost per pound of the mixture is $4.20, so the total cost is:
2.40x + 9.90y = 4.20 * 30
Simplifying the second equation, we get:
2.40x + 9.90y = 126
We can solve this system of equations using substitution, elimination, or a calculator. The solution is x = 24 lbs and y = 6 lbs. Therefore, you will need 24 lbs of the first type of chocolate and 6 lbs of the second type of chocolate to obtain the desired mixture.
The American Community Survey is an ongoing survey that provides data every year to give communities the current information they need to plan investments and services. The 2010 American Community Survey estimates that 14.6% of Americans live below the poverty line, 20.7% speak a language other than English (foreign language) at home, and 4.2% fall into both categories.
a. Draw a Venn diagram summarizing the variables and their associated probabilities
b. What percent of Americans live below the poverty line and only speak English at home?
c. What percent of Americans live below the poverty line or speak a foreign language at home?
Answer:
b. 10.4
c. 26.9
Step-by-step explanation:
Let the universal set U = 100% which is the total no of people in the American community
Let A = 14.6% which is the total no of people living below poverty line
Let B = 20.7% which is the total no of people speaking foreign Language
C = 4.2% no of people who both speak foreign language and live below poverty line
X = no of people who neither live below poverty line nor speak foreign language
P (A) = 14.6%
P (B) = 20.7%
P (C) = P (A ∩ B) = 4.2%
P (A – C) = P (A ∩ U) = 14.6 – 4.2 = 10.4%
P (B – C) = P (B ∩ U) = 20.7 – 4.2 = 16.5%
P (X) = P (A ᴜ B) c =100 – (10.4 + 4.2 + 16.5) = 68.9%
a. The venn diagram is as shown above
b. Percent of Americans who live below poverty line and Speak English at home(minus foreign lang speakers living below poverty line) that is A only
= A – C
= 14.6 – 4.2
= 10.4%
c. Percentage of Americans Living below poverty line or Speaking foreign language
= A only + B only
A only = A – C ( People living below poverty line only)
= 14.6 -4.2
= 10.4%
B only = B – C ( people speaking foreign languages only)
= 20.7 – 4.2
= 16.5%
Hence
A only + B only = 10.4 + 16.5 = 26.9%
According to Scarborough Research, more than 85% of working adults commute by car. Of all U.S. cities, Washington, D.C., and New York City have the longest commute times. A sample of 25 commuters in the Washington, D.C., area yielded the sample mean commute time of 27.97 minutes and sample standard deviation of 10.04 minutes. Construct and interpret a 99% confidence interval for the mean commute time of all commuters in Washington D.C. area.
Answer:
The 99% confidence interval for the mean commute time of all commuters in Washington D.C. area is (22.35, 33.59).
Step-by-step explanation:
The (1 - α) % confidence interval for population mean (μ) is:
[tex]CI=\bar x\pm z_{\alpha /2}\frac{\sigma}{\sqrt{n}}[/tex]
Here the population standard deviation (σ) is not provided. So the confidence interval would be computed using the t-distribution.
The (1 - α) % confidence interval for population mean (μ) using the t-distribution is:
[tex]CI=\bar x\pm t_{\alpha /2,(n-1)}\frac{s}{\sqrt{n}}[/tex]
Given:
[tex]\bar x=27.97\\s=10.04\\n=25\\t_{\alpha /2, (n-1)}=t_{0.01/2, (25-1)}=t_{0.005, 24}=2.797[/tex]
*Use the t-table for the critical value.
Compute the 99% confidence interval as follows:
[tex]CI=27.97\pm 2.797\times\frac{10.04}{\sqrt{25}}\\=27.97\pm5.616\\=(22.354, 33.586)\\\approx(22.35, 33.59)[/tex]
Thus, the 99% confidence interval for the mean commute time of all commuters in Washington D.C. area is (22.35, 33.59).
PLEASE HELP ME
select the most reasonable metric unit for a glass containing 350 units of liquid. Choose from L, mL, kg, g, and mg.
Answer:
mL
Step-by-step explanation:
Ml
A dishwasher has a mean life of 12 years with an estimated standard deviation of 1.25 years ("Appliance life expectancy," 2013). Assume the life of a dishwasher is normally distributed. Find the number of years that the bottom 25% of dishwasher would last.
Answer:
[tex]z=-0.674<\frac{a-12}{1.25}[/tex]
And if we solve for a we got
[tex]a=12 -0.674*1.25=11.157[/tex]
So the value of height that separates the bottom 25% of data from the top 75% is 11.157.
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the mean life of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(12,1.25)[/tex]
Where [tex]\mu=12[/tex] and [tex]\sigma=1.25[/tex]
For this part we want to find a value a, such that we satisfy this condition:
[tex]P(X>a)=0.75[/tex] (a)
[tex]P(X<a)=0.25[/tex] (b)
Both conditions are equivalent on this case. We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.25 of the area on the left and 0.75 of the area on the right it's z=-0.674. On this case P(Z<-0.674)=0.25 and P(z>-0.674)=0.75
If we use condition (b) from previous we have this:
[tex]P(X<a)=P(\frac{X-\mu}{\sigma}<\frac{a-\mu}{\sigma})=0.25[/tex]
[tex]P(z<\frac{a-\mu}{\sigma})=0.25[/tex]
But we know which value of z satisfy the previous equation so then we can do this:
[tex]z=-0.674<\frac{a-12}{1.25}[/tex]
And if we solve for a we got
[tex]a=12 -0.674*1.25=11.157[/tex]
So the value of height that separates the bottom 25% of data from the top 75% is 11.157.
The lifespan of the dishwashers in the bottom 25% is approximately 11.16 years, found by calculating the corresponding value to the 25th percentile z-score from the normal distribution of the appliance's lifespan.
Explanation:The problem is asking for the life of the dishwasher that falls in the bottom 25% of the normally distributed lifespan range. In other words, we need to find the dishwasher lifespan that is the cutoff for the bottom quartile. For a normal distribution, the 25th percentile (the cutoff for the bottom quartile) is commonly found by using a z-score, which is a measure of how many standard deviations a value is from the mean.
The z-score for the 25th percentile is typically -0.675. We can find the lifespan corresponding to this z-score using the formula: lifespan = mean + z*sd. Here, 'mean' is the average lifespan, 'z' is the z-score, and 'sd' is the standard deviation.
Therefore, substituting the known values into the formula, we get: lifespan = 12 + (-0.675)*1.25 = 11.15625 years.
Therefore, the number of years the bottom 25% of dishwashers would last is approximately 11.16 years.
Learn more about Normal Distribution here:https://brainly.com/question/34741155
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Circle H is inscribed with quadrilateral D E F G. Angle E is 123 degrees. The measure of arc D E is 73 degrees. What is the measure of arc EF in circle H? 41° 50° 114° 173°
Answer:
41 degrees
Step-by-step explanation:
step 1
Find the measure of arc DGF
we know that
The inscribed angle is half that of the arc comprising
so
[tex]m\angle E=\frac{1}{2}[arc\ DGF][/tex]
we have
[tex]m\angle E=123^o[/tex]
substitute
[tex]123^o=\frac{1}{2}[arc\ DGF][/tex]
[tex]arc\ DGF=246^o[/tex]
step 2
Find the measure of arc EF
we know that
[tex]arc\ DGF+arc\ DE+arc\ EF=360^o[/tex] ----> by complete circle
substitute the given values
[tex]246^o+73^o+arc\ EF=360^o[/tex]
[tex]319^o+arc\ EF=360^o[/tex]
[tex]arc\ EF=360^o-319^o=41^o[/tex]
Answer: A)41 Degrees
Step-by-step explanation:
It was right on edu 2023
Suppose a struggling student who is currently taking pre-statistics and not passing (60%) wants to predict his introductory statistics course grade. Should the regression line be use to make this prediction?
Answer:
No
Step-by-step explanation:
Because the model was developed using only pre-statistics course grades between 70% and 95% so it is risky to assume that linear trend will continue far beyond that span of values.
Of all airline flight requests received by a certain discount ticket broker, 90% are for domestic travel (D) and 10% are for international flights (I). Let x be the number of requests among the next three requests received that are for domestic flights. Assuming independence of successive requests, determine the probability distribution of x. (Hint: One possible outcome is DID, with the probability (0.9)(0.1)(0.9)
Answer:
Step-by-step explanation:
Given that of all airline flight requests received by a certain discount ticket broker, 90% are for domestic travel (D) and 10% are for international flights (I).
Let x be the number of requests among the next three requests received that are for domestic flights.
X can take values as 0,1, 2 or 3.
Since independence of successive requests is assumed we find that X having two outcomes and independence
X is binomial with n =3 and p= 0.90 (constant for each trial)
PDF of X would be
[tex]P(X=x) = 3Cx (0.9)^r (0.1)^{3-r} , r=0,1,2,3[/tex]
Thus pdf of X is
X 0 1 2 3
p 0.001 0.027 0.243 0.729
Final answer:
The probability distribution of x, where x is the number of domestic flight requests among the next three requests, follows a binomial distribution with n=3 and p=0.9. It can be calculated using the formula for binomial probabilities, considering the value of x can be 0, 1, 2, or 3. We get P = 0.081.
Explanation:
The question involves calculating the probability distribution of the random variable x, which represents the number of domestic flight requests among the next three requests received by a discount ticket broker. Since each request is independent and only two outcomes are possible (domestic or international), a binomial distribution can be used to determine the probabilities for x. For instance, the probability for one particular sequence of requests such as DID (domestic, international, domestic) is calculated as (0.9)(0.1)(0.9), which is the product of the probabilities for each request in that sequence. To find the probability distribution of x, we consider all possible sequences of three requests and their associated probabilities, which are determined by multiplying the individual probabilities for each request in the sequence following the rules of binomial distribution.
The random variable x can take on the following values: 0, 1, 2, or 3, representing the number of domestic flight requests out of three. We calculate probabilities for each of these values using the binomial formula:
[tex]P(x=0) = (0.1)^3\\P(x=1) = 3 * (0.9)(0.1)^2\\P(x=2) = 3 * (0.9)^2(0.1)\\P(x=3) = (0.9)^3[/tex]
P = 0.081.
In a past presidential election, it was estimated that the probability that the Republican candidate would be elected was 5/7, and therefore the probability that the Democratic candidate would be elected was 2/7 (the two Independent candidates were given no chance of being elected). It was also estimated that if the Republican candidate were elected, the probability that a conservative, moderate, or liberal judge would be appointed to the Supreme Court (one retirement was expected during the presidential term) was 1/7, 1/7, and 5/7, respectively. If the Democratic candidate were elected, the probabilities that a conservative, moderate, or liberal judge would be appointed to the Supreme Court would be 1/3, 1/6, and 1/2, respectively. A conservative judge was appointed to the Supreme Court during the presidential term. What is the probability that the Democratic candidate was elected
Answer:
The probability that the Democratic candidate was elected given that a conservative judge was appointed to the Supreme Court is [tex]\frac{14}{29}[/tex].
Step-by-step explanation:
The conditional probability of an events A given that another events B has already occurred is given by:
[tex]P(A|B)=\frac{P(B|A)P(A)}{P(B|A)P(A)+P(B|A^{c})P(A^{c})}[/tex]
The estimation of the past presidential election is provided.
Denote the events as follows:
R = a Republican candidate would be elected
D = a Democratic candidate would be elected
C = a conservative judge would be appointed to the Supreme Court
M = a moderate judge would be appointed to the Supreme Court
L = a liberal judge would be appointed to the Supreme Court
The information provided is:
[tex]P(R)=\frac{5}{7},\ P(D)=\frac{2}{7}[/tex]
[tex]P(C|R)=\frac{1}{7},\ P(M|R)=\frac{1}{7},\ P(L|R)=\frac{5}{7}[/tex]
[tex]P(C|B)=\frac{1}{3},\ P(M|D)=\frac{1}{6},\ P(L|D)=\frac{1}{2}[/tex]
It is provided that a conservative judge was appointed to the Supreme Court during the presidential term.
Compute the probability that the Democratic candidate was elected given that a conservative judge was appointed to the Supreme Court as follows:
[tex]P(D|C)=\frac{P(C|D)P(D)}{P(C|D)P(D)+P(C|R)P(R)}[/tex]
[tex]=\frac{(\frac{1}{3}\times \frac{2}{7})}{(\frac{1}{3}\times \frac{2}{7})+(\frac{1}{7}\times \frac{5}{7})}[/tex]
[tex]=\frac{\frac{2}{21}}{\frac{2}{21}+\frac{5}{49}}[/tex]
[tex]=\frac{2}{21}\div \frac{29}{147}[/tex]
[tex]=\frac{14}{29}[/tex]
Thus, the probability that the Democratic candidate was elected given that a conservative judge was appointed to the Supreme Court is [tex]\frac{14}{29}[/tex].
What is the solution
2 – 3y=1
x – 2y = 6
Answer: x = - 16
y = - 11
Step-by-step explanation:
The given system of linear equations is expressed as
2x - 3y = 1- - - - - - - - - - - - -1
x - 2y = 6 - - - - - - - - - - - -2
We would eliminate x by multiplying equation 1 by 1 and equation 2 by 2. It becomes
2x - 3y = 1- - - - - - - - - - -3
2x - 4y = 12- - - - - - - - - - - -4
Subtracting equation 4 from equation 3, it becomes
y = - 11
Substituting y = - 11 into equation 2, it becomes
x - 2 × - 11 = 6
x + 22 = 6
Subtracting 22 from the left hand side and the right hand side of the equation, it becomes
x + 22 - 22 = 6 - 22
x = - 16
Functionally important traits in animals tend to vary little from one individual to the next within populations, possible because individuals that deviate too much from the mean die sooner or leave fewer offspring in the long run. If so, does variance in a trait rise after it becomes less functionally important? Billet et al. (2012) investigated this question with the semicircular canals (SC) of the inner ear of the three-toed sloth (Bradypus variegatus). Sloths move very slowly and infrequently, and the authors suggested that this behavior reduces the functional demands on the SC, which usually provide information on angular head movement to the brain. Indeed, the motion signal from the SC to the brain may be very weak in sloths as compared to faster-moving animals. The following numbers are measurements of the length to the width of the anterior semicircular canals in seven sloths. Assume that this represents a random sample.
1.52, 1.06, 0.93, 1.38, 1.47, 1.20, 1.16
a. In related, faster-moving animals, the standard deviation of the ratio of the length to the width of the anterior semicircular canals is known to be 0.09. What is the estimate of the standard deviation of this measurement in three toed sloths?
b. Based on these data, what is the most plausible range of values for the population standard deviation in the three-toed sloth? Does this range include the known value of the standard deviation in related, faster-moving species?
c. What additional assumption is required for your answer in (b)? What do you know about how sensitive the confidence interval calculation is when the assumption is not met?
Answer:
Step-by-step explanation:
Hello!
The objective is to study the semicircular canals (SC) of the inner ear of the three-toed sloth (Bradypus variegatus) to see if it is weak compared to faster animals.
The study variable is X: length to width of the anterior semicircular canal of a three-toed sloth.
A sample of 7 sloths was taken and the semicircular canal was measured:
1.52, 1.06, 0.93, 1.38, 1.47, 1.20, 1.16
∑X= 8.72
∑X²= 11.15
a.
[tex]S^2= \frac{1}{n-1} * [sumX^2-\frac{(sumX)^2}{n} ]= \frac{1}{6} *[11.15-\frac{(8.72)^2}{7} ][/tex]
S²= 0.047≅0.05
S=0.218≅ 0.22
Comparing the estimation of the variance of the length to width of the anterior semicircular canal of three-toed sloths with the known number of length to width of the anterior semicircular canal of faster animals (S=0.09), it appears that the variability os length to width of the anterior semicircular canal of sloths is greater than the length to width of the anterior semicircular canal of faster animals.
b. and c.
To estimate the most plausible range of values of the population standard deviation of the anterior semicircular canal of the sloths, you have to do an estimation per confidence interval.
To be able to make this estimation we have to assume that the variable of interest has a normal distribution. With this assumption, it is valid to use a Chi-Square statistic to estimate the population standard deviation.
[tex]X^2= \frac{(n-1)S^2}{Sigma^2} ~X^2_{n-1}[/tex]
I'll choose a confidence level of 95%
The formula for the interval is:
[tex][\frac{(n-1)S^2}{X^2_{n-1;1-\alpha /2}} ;\frac{(n-1)S^2}{X^2_{n-1;\alpha /2}} ][/tex]
[tex]X^2_{n-1;1-\alpha /2}= X^2_{6;0.975}= 14.449[/tex]
[tex]X^2_{n-1;\alpha /2}}= X^2_{6;0.025}= 1.2373[/tex]
[tex][\frac{6*0.05}{14.449} +\frac{6*0.05}{1.2373} ][/tex]
[0.2076;2.4246] ⇒This confidence interval is for the population variance, calculating the square root of each bond gives us the CI for the population standard deviation:
√[0.2076;2.4246]= [0.1441;1.5571]
The 95% CI [0.1441;1.5571] is expected to contain the true value of the population standard deviation of the length to width of the anterior semicircular canal of the three-toed sloths.
As you can see this interval does not contain the known value of the population standard deviation for faster animals, which leads to thinking there is a difference between the standard deviation of the anterior semicircular canal in both species.
I hope it helps!
Which of the following when added to 4a^2+9 will result in a perfect square for all integer values of a?
(A) 0
(B) 3a
(C) 6a
(D) 9a
(E) 12a
Answer:
(D) 9a
Step-by-step explanation:
Given
4a^2 + 9
Add 9a to the expression
4a^2 + 9 + 9a
This can be written as
(2a)^2 + (3)^2 + (3)^2 a
Answer:
E. 12a
Step-by-step explanation:
TBH no idea why thats correct.
Sean, a high school wrestler, has agreed to participate in a study of cardiovascular conditioning. He is left somewhat confused when, at the first research session, he is asked to complete a questionnaire about commonly purchased grocery items. Sean's confusion indicates a lack of ________ regarding the task. Question 2
Answer:
Face validity.
Step-by-step explanation:
Face validity is considered the weakest form of validity as it does a superficial, subjective assessment which does not involve objective approach, revealing the deeper intent of the test being used. It involved a process similar to skimming the surface of an item or a book to make opinions. Though it is a weak form of validity, it is the easiest to apply to research. Face validity is an informal approach to identifying how suitable the content of a test is to the research.
It generally asks the question:
Is the content of the test suitable to its aims?
Suppose that 15% of the fields in a given agricultural area are infested with the sweet potato whitefly. One hundred fields in this area are randomly selected and checked for whitefly. Based on your knowledge of the empirical rule, within what limits would you expect to find the number of infested fields, with probability approximately 95%? (Round your answers to three decimal places.) 4.29 X fields to 25.71 x fields What might you conclude if you found that x = 45 fields were infested? Is it possible that one of the characteristics of a binomial experiment is not satisfied in this experiment? Explain.
A. Based on limits above, it is unlikely that we would see x = 45, so it might be possible that the trials are not independent. O
B. Based on the limits above, it is unlikely that we would see x = 45, so it might be possible that the trials have more than two possible outcomes.
C. Based on the limits above, it is unlikely that we would see x = 45, so it might be possible that there are an indefinite number of trials.
D. Based on the limits above, it is likely that we would see x = 45, so all of the characteristics of a binomial experiment are satisfied.
Answer:
a.[tex]\mu=15[/tex]
b.[tex]\mu=7.8586 \ and \ \mu=22.1414[/tex]
c. Choice A- Based on limits above, it is unlikely that we would see x = 45, so it might be possible that the trials are not independent.
Step-by-step explanation:
a.Binomial distribution is defined by the expression
[tex]P(X=k)=C_k^n.p^k.(1-p)^{n-k}[/tex]
Let n be the number of trials,[tex]n=100[/tex]
and p be the probability of success,[tex]p=15\%[/tex]
The mean of a binomial distribution is the probability x sample size.
[tex]\mu=np=100\times0.15=15[/tex]
b.Limits within which p is approximately 95%
sd of a binomial distribution is given as:[tex]\sigma=\sqrt npq\\q=1-p[/tex]
Therefore, [tex]\sigma=\sqrt(100\times0.015\times0.85)=3.5707[/tex]
Use the empirical rule to find the limits. From the rule, approximately 95% of the observations are within to standard deviations from mean.
[tex]sd_1=>\mu-2\sigma=15-2\times3.3507=7.8586\\sd_2=>\mu-2\sigma=15+2\times3.3507=22.1414[/tex]
Hence, approximately 95% of the observations are within 7.8586 and 22.1414 (areas of infestation).
c. [tex]x=45[/tex] is not within the limits in b above (7.8586,22.1414). X=45 appears to be a large area of infestation. A.Based on limits above, it is unlikely that we would see x = 45, so it might be possible that the trials are not independent.
Final answer:
Using the empirical rule, we can determine the limits within which we would expect to find the number of infested fields with a 95% probability. If we found a number of infested fields that is higher than expected, it suggests that one of the characteristics of a binomial experiment may not be satisfied. Correct answer is B.
Explanation:
In this problem, we are given that 15% of the fields in a given agricultural area are infested with the sweet potato whitefly. We are asked to determine the limits within which we would expect to find the number of infested fields with a probability of approximately 95%. This situation can be modeled using the binomial distribution, as each field can be considered as a separate trial with two possible outcomes, infested or not infested.
According to the empirical rule, for a binomial distribution, we can expect about 95% of the outcomes to fall within two standard deviations of the mean. The mean number of infested fields can be calculated as 15% of the total number of fields, which is 15. The standard deviation of the number of infested fields can be determined using the formula σ = [tex]\sqrt{(npq)}[/tex], where n is the number of trials, p is the probability of success, and q is the probability of failure. In this case, n = 100, p = 0.15, and q = 0.85.
Using these values, we can calculate the standard deviation as σ = [tex]\sqrt{(100 * 0.15 * 0.85)}[/tex] ≈ 3.150. Therefore, we would expect to find about 95% of the number of infested fields within two standard deviations of the mean, which is between 15 - (2 * 3.150) = 8.700 and 15 + (2 * 3.150) = 21.300.
If we found that x = 45 fields were infested, we can conclude that this number is higher than what we would expect based on the binomial distribution. It is unlikely to observe such a high number of infested fields if the trials were independent and had only two possible outcomes. Therefore, we might suspect that one of the characteristics of a binomial experiment is not satisfied in this experiment.
Based on the limits above, it is unlikely that we would see x = 45, so it might be possible that the trials have more than two possible outcomes. Therefore, the correct answer is B.
Determine whether the argument is valid or invalid.
Loretta's hobby is stamp collecting. If her husband likes to fish, then Loretta's hobby is not stamp collecting. If her husband does not like to fish, then Nathan likes to read. Therefore, Nathan likes to read.
Answer:
The argument is valid.
Step-by-step explanation:
We are told "Loretta's hobby is stamp collecting."
"If her husband likes to fish, then Loretta's hobby is not stamp collecting."
Her hobby is stamp collecting, so her husband does not like to fish.
"If her husband does not like to fish, then Nathan likes to read."
Her husband does not like to fish; therefore, Nathan likes to read.
The argument is valid.
The argument is invalid as it fails the informal test of validity; the premises about Loretta and her husband's hobbies do not logically lead to the conclusion about Nathan's reading habits.
Explanation:The task involves assessing the validity of an argument by applying the informal test of validity. Let's deconstruct the argument provided. It states that Loretta's hobby is stamp collecting, and presents two conditional statements involving her husband's hobbies and Nathan's interest. Finally, it concludes that Nathan likes to read.
To apply the informal test of validity, we must determine if it's possible for all premises to be true while the conclusion could still be false. In this argument, even if all the stated conditions about Loretta and her husband's hobbies are true, they don't logically necessitate the conclusion about Nathan's reading habits. Thus, the argument is invalid because it's possible to imagine a scenario where all premises are true, but Nathan does not like to read. The premises about Loretta and her husband have no logical connection to Nathan's interests, making it invalid.
A valid argument ensures that if the premises are true, the conclusion must also be true. However, this argument fails to meet that criterion, indicating its invalidity based on the informal test.
i really need help:(
Answer: the height of the building is 40ft
Step-by-step explanation:
Looking at the right angle triangle formed,
With angle P as the reference angle, the length shadow of the building on ground represents the adjacent side of the right angle triangle.
The height of the building represents the opposite side of the right angle triangle.
a) to determine the height of the building, x, we would apply the tangent trigonometric ratio which is expressed as
Tan θ, = opposite side/adjacent side. Therefore, the equation becomes
Tan P = x/50
b) 0.8 = x/50
x = 50 × 0.8
x = 40 ft