At one SAT test site students taking the test for a second time volunteered to inhale supplemental oxygen for 10 minutes before the test. In fact, some received oxygen, but others (randomly assigned) were given just normal air. Test results showed that 42 of 66 students who breathed oxygen improved their SAT scores, compared to only 35 of 63 students who did not get the oxygen. Which procedure should we use to see if there is evidence that breathing extra oxygen can help test-takers think more clearly

Multiple linear regression can be said to be a statistical technique that uses several explanatory variables to predict the outcome of a response variable.

The Formula for Multiple Linear Regression Is

yi= β0+β1xi1+β2xi2+...+βpxip+ϵ

​

where, for i=n observations

yi​= Dependent variable

xi​= Expanatory variable

β0​= y - intercept (constant term)

βp​= Slope coefficients for each explanatory variable

ϵ= The model’s error term (also known as the residuals)​

From the question written above,

yi= weight gain which is dependent on the explanatory variables which are hemoglobin change, tap water consumption, and age. i.e. xi

Model assumptions

1. There is a linear relationship between the dependent variables and the independent variables.

2. The independent variables are not too highly correlated with each other.

3. yi observations are selected independently and randomly from the population.

4. Residuals should be normally distributed with a mean of 0 and variance σ.

(Investopedia, 2019)

Answer:

The z statistic is 0.23.

Step-by-step explanation:

Test statistic (z) = (sample mean - population mean) ÷ sd/√n

sample mean = 104 mg

population mean (mu) = 100 mg

sd = 55 mg

n = 10

z = (104 - 100) ÷ 55/√10 = 4 ÷ 17.393 = 0.23

Final answer:

The z-statistic for the given hypothesis test is calculated based on the sample mean, population standard deviation, and sample size.

Explanation:

The z-statistic for this hypothesis test can be calculated using the sample mean, population standard deviation, and sample size.

Given that the sample mean is 104 mg, population standard deviation is 55 mg, and sample size is 10 pills, the z-statistic is calculated as (104 - 100) / (55 / sqrt(10)), which equals 0.8.

Therefore, the correct z-statistic for this scenario is 0.80.

To find the probability of different scenarios involving defective components produced by a certain process, we can use the Poisson and binomial distributions.

(a) To find the probability that exactly 15 defective components are produced, we can use the formula for the Poisson distribution:

P(X=k) = (e^(-λ) * λ^k) / k!

Here, λ is the mean number of defective components produced in one day, which is 20. So, λ = 20. Substituting this value into the formula, we get:

P(X=15) = (e^(-20) * 20^15) / 15!

Calculating this expression will give us the probability.

(b) To find the probability that exactly 10 of the 15 defective components are repairable, we can use the binomial distribution since each defective component has a fixed probability of being repairable. Here, the number of trials is 15, and the probability of success (being repairable) is 0.60. Substituting these values into the binomial distribution formula, we can calculate the probability.

(c) Given the value of N, the number of defective components produced, X has a binomial distribution since X represents the number of repairable defective components. The probability of each component being repairable is constant, so it follows a binomial distribution.

(d) To find the probability that exactly 15 defective components are produced, with exactly 10 of them being repairable, we can multiply the probabilities obtained from parts (a) and (b) together, since these events are independent. Multiplying the results will give us the desired probability.

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(a) The probability that exactly 15 defective components are produced is 0.0516

(b) Given that exactly 15 defective components are produced, the probability that exactly 10 of them are repairable is 0.1241.

(c) Given the value of N, X follows a binomial distribution

(d) The probability that exactly 15 defective components are produced, with exactly 10 of them being repairable is 0.0064.

(a) Probability of Exactly 15 Defective Components

A Poisson distribution with mean λ = 20 is used. The formula is:

[tex]P(X = k) = (e^{(-\lambda)} * \lambda^k) / k![/tex]

For k = 15 and λ = 20:

[tex]P(X = k) = (e^{(-20)} * 20^15) / 15! \approx 0.0516[/tex]

(b) Probability that Exactly 10 Out of 15 Defective Components are Repairable

This scenario uses a binomial distribution.

Given N = 15 defectives, the probability that exactly 10 are repairable (with p = 0.60) is:

[tex]P(X = 10 | N = 15) = C(15,10) * 0.6^{10} * 0.4^{5} \approx 0.1241[/tex]

(c) Distribution of X Given N

Given N = n

X (number of repairable components) follows a binomial distribution Bin(n, 0.60).

So, X | N = n follows Bin(n, 0.60).

(d) Probability of 15 Defective Components with Exactly 10 being Repairable

The joint probability is the product of the Poisson and binomial probabilities:

[tex]P(X = 15) * P(Y = 10 | X = 15)= 0.0516 * 0.1241 \approx 0.0064[/tex]

Answer:

The standard error for the mean finish time of 30 randomly selected participants is 0.055 hours

Step-by-step explanation:

Standard error = sample standard deviation ÷ sqrt (sample size)

sample standard deviation = 0.30 hours

sample size = 30

standard error = 0.30 ÷ sqrt(30) = 0.30 ÷ 5.477 = 0.055 hours

Answer:

Width = 25

Length = 25

Area = 625

Step-by-step explanation:

The perimeter of a rectangle is given by the sum of its four sides (2L+2W) while the area is given by the product of the its length by its width (LW). It is possible to write the area as a function of width as follows:

[tex]100 = 2L+2W\\L = 50-W\\A=LW=W*(50-W)\\A=50W - W^2[/tex]

The value of W for which the derivate of the area function is zero is the width that yields the maximum area:

[tex]A=50W - W^2\\\frac{dA}{dW}=0=50 - 2W\\ W=25[/tex]

With the value of the width, the length (L) and the area (A) can be also be found:

[tex]L=50-25 = 25\\A=W*L=25*25\\A=625[/tex]

Since the values satisfy the condition W≤L, the answer is:

Width = 25

Length = 25

Area = 625

Answer:

The service line is J9263 x 300 to report a unit of 150(300x 0.5 mg = 150).                    

Step-by-step explanation:

The drug J9263 Eloxatin contains 0.5 mg oxaliplatain.

For a infusion of 50 mg the unit reported for service line information is:

- Service line: J9263 x 100

- Unit reported for service line information: 50 = 100 x 0.5 mg

Hence, for a infusion of 150 mg, the unit reported for service line information is:

- Unit reported: 150(300 x 0.5 mg = 150)

- Service line information: J9263 x 300

Therefore, if the physician provided 150 mg infusion of the drug instead of an injection the service line is J9263 x 300 to report a unit of 150(300x 0.5 mg = 150).

I hope it helps you!                          

The unit reported for service line information for 150 mg infusion based on the injection description is :

Given the injection description :

For 150 mg infusion :

Unit reported would be:

Therefore, the service line information and the unit reported would be:

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Answer:

81.2 is the 62th percentile

Step-by-step explanation:

What is the interpretation for a percentile?

When a value V is said to be in the xth percentile of a set, x% of the values in the set are lower than V and (100-x)% of the values in the set are higher than V.

300 observations, there are 186 points less than 81.2. Find the percentile for 81.2.

So

[tex]p = \frac{186}{300} = 0.62[/tex]

81.2 is the 62th percentile

Answer: there were 40 questions on her math final.

Step-by-step explanation:

Let x represent the total number of questions in the math test.

Mary got 85% correct on her math test. This means that the number of questions that she got right is

85/100 × x = 0.85 × x = 0.85x

This also means that the number of questions that she missed would be

x - 0.85x = 0.15x

Therefore, if Mary missed 6 questions, it means that

0.15x = 6

Dividing both sides of the equation by 0.15, it becomes

0.15x/0.15 = 6/0.15

x = 40

Answer:

Step-by-step explanation:

                    1

                1      1

            1      2      1

         1     3      3      1

      1    4     6       4       1

   1   5    10     10       5     1

 1    6   15   20      15    6     1

1    6   15   20      15    6     1

we use these for the expansion of (5x² + 2y³)⁶

1(5x²)⁶(2y³)⁰ + 6(5x²)⁵(2y³)¹ + 15(5x²)⁴(2y³)² + 20(5x²)³(2y³)³+  15(5x²)²(2y³)⁴+ 6(5x²)¹(2y³)⁵ + 1(5x²)⁰(2y³)⁶

78125ₓ¹²+187500ₓ¹⁰ y³ +37500ₓ⁸y⁶+20000ₓ⁶y⁹+6000x⁴y¹²+960x²y¹⁵+2y¹⁸

a.)a = 6, b = 9. the coefficient of xᵃyᵇ ( 20000ₓ⁶y⁹) = 20000

b) a = 2, b = 15. the coefficient of xᵃyᵇ ( 960x²y¹⁵) = 960

c) a = 3, b = 12. the coefficient of xᵃyᵇ is not present

d) a = 12, b = 0 the coefficient of xᵃyᵇ ( 78125ₓ¹²)  = 78125

e) a = 8, b = 9. the coefficient of xᵃyᵇ is not present

The coefficients of xᵃyᵇ for respective given values of a and b have been provided below.

We are given the expression;

(5x² + 2y³)⁶

Using online binomial expansion calculator gives us;

15625x¹² + 37500x¹⁰y³ + 37500x⁸y⁶ + 20000x⁶y⁹ + 6000x⁴y¹² + 960x²y¹⁵ + 64y¹⁸

We want to find the coefficient of xᵃyᵇ in the binomial expansion;

1) When a = 6 and b = 9, the coefficient is 20000

2) When a = 2, b = 15; the coefficient is 960

3) When a = 3 and b = 12; there is no coefficient

4) When a = 12 and b = 0; the coefficient is 15625

5) When a = 8 and b = 9; there is no coefficient.

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Answer:

a. x= $6, y= $8

b. z= $2

Step-by-step explanation:

at equilibrium, the marginal utility per dollar spent will be equal i.e

zA=zB

20-3x=18-2y

upon simplification, we arrive at

[tex]x=\frac{2}{3} (1+y)\\[/tex]......equation 1

since the total amount to spend is $14, then

x+y=14

x=14-y..............equation 2

if we solve equation 1 and equation 2 simultaneously

[tex]14-y=\frac{2}{3} (1+y)\\42-3y=2+2y\\5y=40\\y=8[/tex]

Hence for y=8

x=14-y=14-8

x=6

Hence the amount spent on Product A is $6 and the amount spent on product B is $8

b. to determine the amount of utility the marginal dollar will yield, we substitute the values of y and x into the the given equation,

zA=20-3x=20-3(6)

zA=20-18=2

zB=18-2y=18-2(8)

zB=18-16=2

hence the amount spent on the marginal utility is $2

Step-by-step explanation:

Let x be line xy.

y represents line zm.

z is line zx or line zy

The area of one of the smaller triangles is x/2* y.

same for the other triangle.

The perimeter for either one of the triangles is x/2+y+z.

"You do not eat tofu" is derived using the Modus Tollens rule of inference.

The rule of inference that is used to derive the conclusion "You do not eat tofu" from the given statements is Modus Tollens.

Modus Tollens is a valid deductive argument form that follows this structure:

1. If P, then Q.

2. Not Q.

3. Therefore, not P.

The statements correspond to:

1. For all x, if x is healthy to eat, then x does not taste good.

2. Tofu is healthy to eat.

3. You only eat what tastes good.

Using these statements, we can infer:

1. If tofu is healthy to eat, then tofu does not taste good. (From statement 1)

2. Tofu does not taste good. (From statement 2 and the derived inference)

3. Therefore, you do not eat tofu. (Using Modus Tollens with statement 3 and the derived inference)

So, the conclusion "You do not eat tofu" is derived using the Modus Tollens rule of inference.

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Final answer:

The rule of inference used to derive the conclusion 'You do not eat tofu' is called Modus Tollens, which allows to deduce that if 'p implies q' is true and 'q' is false, then 'p' must also be false.

Explanation:

The student is asking about a logical inference rule used to derive a conclusion from a set of premises. Considering the provided statements, which can be summarized as:

For all x, if x is healthy to eat, then x does not taste good (All healthy foods taste bad).

Tofu is healthy to eat.

You only eat what tastes good.

We can see that the rule of inference used here is Modus Tollens. This rule of inference suggests that if we have a conditional statement (if p then q) and it is given that the consequent q is false (not q), then the antecedent p must also be false (not p).

To apply Modus Tollens:

Translate the given information into logical statements:
a) If something is healthy (p) then it does not taste good (q).
b) Tofu is healthy (p).
c) You do not eat what does not taste good (¬q).

Since tofu is healthy (p), it does not taste good as per the given rule (therefore, q is true). But the third statement says you do not eat what does not taste good, meaning (¬q). If (¬q) is valid, then by Modus Tollens, you do not eat tofu (¬p).

Thus, the usage of Modus Tollens allows us to infer that 'You do not eat tofu' from the given premises.

Answer:

See explanation to get answer.

Step-by-step explanation:

Solution

As per the data and information given in the question, there are three Bidders, one each on Monday, Tuesday and Wednesday.

Bidder 1 may bid on Monday either for $2,000,000 or $3,000,000 with probabilities 0.5 each

Therefore expected pay-off for Bidder 1 is $2,500,000 (2,000,000*.52 + 3,000,000*.5)

Bidder 2 may bid on Tuesday either for $2,000,000 with probability 0.9 or $4,000,000 with probability 0.1

Therefore expected pay-off for Bidder 2 is $2,200,000 (2,000,000*.9 + 4,000,000*.1)

Bidder 3 may bid on Wednesday either for $1,000,000 with probability 0.7 or for $4,000,000 with probability 0.3

Therefore expected pay-off for Bidder 3 is $1,900,000 (1,000,000*.7 + 4,000,000*.3)

Based on the comparison of the above mentioned calculations for the expected pay-off for the bidders, it is recommended that the optimal decision strategy among the bidders is to go for Bidder 1 with highest expected pay-off of $2,500,000 and accept the bid of Bidder 1.

Risk profile for the optimal solution is $2,000,000 with probability 0.5 and $3,000,000 with probability 0.5

Bid may be for $4,000,000 with probability of 0.1 by Bidder 2 or with probability 0.3 by Bidder 3

Answer:

The value of test statistic is 1.338

Step-by-step explanation:

We are given the following in the question:  

Population mean, μ = 16.000

Sample mean, [tex]\bar{x}[/tex] = 16.218

Sample size, n = 22

Alpha, α = 0.05

Sample standard deviation, s = 0.764

First, we design the null and the alternate hypothesis

[tex]H_{0}: \mu = 16.000\text{ cm}\\H_A: \mu < 16.000\text{ cm}[/tex]

We use one-tailed t test to perform this hypothesis.

Formula:

[tex]t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }[/tex]

Putting all the values, we have

[tex]t_{stat} = \displaystyle\frac{16.218 - 16.000}{\frac{0.764}{\sqrt{22}} } = 1.338[/tex]

Thus, the value of test statistic is 1.338

Answer:

0.06597

Step-by-step explanation:

Given that thirty-seven percent of the American population has blood type O+

Five Americans are tested for blood group.

Assuming these five Americans are not related, we can say that each person is independent of the other to have O+ blood group.

Also probability of any one having this blood group = p = 0.37

So X no of Americans out of five who were having this blood group is binomial with p =0.37 and n =5

Required probability

=The probability that at least four of the next five Americans tested will have blood type O+

= [tex]P(X\geq 4)\\= P(X=4)+P(x=5)\\= 5C4 (0.37)^4 (1-0.37) + 5C5 (0.37)^5\\= 0.06597[/tex]

Answer:

Required probability = 0.066

Step-by-step explanation:

We are given that Thirty-seven percent of the American population has blood type O+.

Firstly, the binomial probability is given by;

[tex]P(X=r) =\binom{n}{r}p^{r}(1-p)^{n-r} for x = 0,1,2,3,....[/tex]

where, n = number of trails(samples) taken = 5 Americans

           r = number of successes = at least four

           p = probability of success and success in our question is % of

                 the American population having blood type O+ , i.e. 37%.

Let X = Number of people tested having blood type O+

So, X ~ [tex]Binom(n=5,p=0.37)[/tex]

So, probability that at least four of the next five Americans tested will have blood type O+ = P(X >= 4)

P(X >= 4) = P(X = 4) + P(X = 5)

                = [tex]\binom{5}{4}0.37^{4}(1-0.37)^{5-4} + \binom{5}{5}0.37^{5}(1-0.37)^{5-5}[/tex]

                = [tex]5*0.37^{4}*0.63^{1} +1*0.37^{5}*1[/tex] = 0.066.

Answer:

Option D) The data are continuous because the data can take on any value in an interval          

Step-by-step explanation:

Discrete Data:

Continuous data:

The volumes (in cubic feet) of different rooms

Since the volume can be expressed in decimals, it can take all the values within an interval. Also volume is measured not counted. Hence, it is a continuous variable.

Thus, the correct answer is:

Option D) The data are continuous because the data can take on any value in an interval

Final answer:

The correct answer is D: The data are continuous because the data can take on any value in an interval.

Explanation:

The volumes (in cubic feet) of different rooms would be considered continuous data because they can take on any value within an interval.

Unlike discrete data, which can only take on specific counting numbers, continuous data includes an infinite number of potential values.

For instance, a room can have a volume of 500.5 cubic feet, 500.55 cubic feet, 500.555 cubic feet, and so forth.

This level of precision is due to the fact that volume is a measurable attribute that does not have to be a whole number and can include fractions or decimals as well.

Therefore, the correct answer is D: The data are continuous because the data can take on any value in an interval.

Answer:

The value of [tex]\bar d[/tex] is -0.2.

The value of [tex]s_{\bar d}[/tex] is 0.3464.

[tex]\mu_{d}[/tex] = mean difference in body temperatures.

Step-by-step explanation:

The data for body temperatures from five different subjects measured at 8 AM and again at 12 AM are provided.

The formula of [tex]\bar d[/tex] and [tex]s_{\bar d}[/tex] are:

[tex]\bar d=\frac{1}{n}\sum (x_{1}-x_{2})[/tex]

[tex]s_{\bar d}=\sqrt{\frac{1}{n-1}\sum (d_{i}-\bar d)^{2}}[/tex]

Consider the table below.

Compute the value of [tex]\bar d[/tex] as follows:

[tex]\bar d=\frac{1}{n}\sum (x_{1}-x_{2})=\frac{1}{5}\times-1=-0.2[/tex]

Thus, the value of [tex]\bar d[/tex] is -0.2.

Compute the value of [tex]s_{\bar d}[/tex] as follows:

[tex]s_{\bar d}=\sqrt{\frac{1}{n-1}\sum (d_{i}-\bar d)^{2}}=\sqrt{\frac{0.48}{4}}=0.3464[/tex]

Thus, the value of [tex]s_{\bar d}[/tex] is 0.3464.

The variable [tex]\mu_{d}[/tex] represents the mean difference in body temperatures  measured at 8 AM and again at 12 AM.

Answer:

The relation represents y as a function of x, because each value of x is associated with a single value of y.

Answer:

a) 0.9961

b) 0.9886          

Step-by-step explanation:

We are given the following information:

We treat passenger not showing up as a success.

P(passenger not showing up) = 0.10

Then the number of passengers follows a binomial distribution, where

[tex]P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}[/tex]

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 125

a) probability that every passenger who shows up can take the flight

[tex]P(x \geq 5) = 1- P(x = 0) - P(x = 1)-P(x = 2) - P(x = 3) - P(x = 4) \\= 1-\binom{125}{0}(0.10)^0(1-0.10)^{125} -...-\binom{125}{4}(0.10)^4(1-0.10)^{121}\\=0.9961[/tex]

b)  probability that the flight departs with empty seats

[tex]P(x > 5) =P(x\geq 5) - P(x = 5) \\= 0.9961 -\binom{125}{5}(0.10)^5(1-0.10)^{120}\\=0.9961-0.0075\\ = 0.9886[/tex]

Answer:

0.717 or 71.7%

Step-by-step explanation:

P(M) = 0.852

P(D) = 0.759

P(M or D) = 0.894

The probability that a randomly selected American has both medical and dental insurance is given by the probability of having medical insurance, added to the probability of having dental insurance, minus the probability of having either insurance:

[tex]P(M\ and\ D) = P(M)+P(D)-P(M\ or\ D)\\P(M\ and\ D) =0.852+0.759-0.894\\P(M\ and\ D) =0.717=71.7\%[/tex]

The probability is 0.717 or 71.7%.

The result is a 71.7% probability of an adult American having both insurances.

The question revolves around finding the probability of a randomly selected adult American having both medical and dental insurance. To calculate this, we use the principle of inclusion-exclusion. According to the problem statement, the percentage of adults with medical insurance is 85.2%, with dental insurance is 75.9%, and with either of the two is 89.4%. The principle of inclusion-exclusion states that the probability of the union of two events (medical or dental insurance) is equal to the sum of the probabilities of each event minus the probability of their intersection (both insurances).

Let's denote the following:

Using the principle of inclusion-exclusion, we find P(Medical and Dental) as follows:

P(Medical and Dental) = P(Medical) + P(Dental) - P(Medical or Dental)

P(Medical and Dental) = 85.2% + 75.9% - 89.4%

P(Medical and Dental) = 160.1% - 89.4%

P(Medical and Dental) = 71.7%

Therefore, the probability that a randomly selected adult American will have both medical and dental insurance is 71.7%.

Answer:

For k = 6 or k = -6, the equation will have exactly one solution.

Step-by-step explanation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = (x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]\bigtriangleup = b^{2} - 4ac[/tex]

If [tex]\bigtriangleup = 0[/tex], the equation has only one solution.

In this problem, we have that:

[tex]3x^{2} + kx + 3 = 0[/tex]

So

[tex]a = 3, b = k, c = 3[/tex]

[tex]\bigtriangleup = b^{2} - 4ac[/tex]

[tex]\bigtriangleup = k^{2} - 4*3*3[/tex]

[tex]\bigtriangleup = k^{2} - 36[/tex]

We will only have one solution if [tex]\bigtriangleup = 0[/tex]. So

[tex]\bigtriangleup = 0[/tex]

[tex]k^{2} - 36 = 0[/tex]

[tex]k^{2} = 36[/tex]

[tex]k = \pm \sqrt{36}[/tex]

[tex]k = \pm 6[/tex]

For k = 6 or k = -6, the equation will have exactly one solution.

When [tex]x=3[/tex], we get the parabola

[tex]z=-4-2y^2[/tex]

We can parameterize this parabola by

[tex]\vec r(t)=(3,t,-4-2t^2)[/tex]

Then the tangent vector to this parabola is

[tex]\vec T(t)=\dfrac{\mathrm d\vec r(t)}{\mathrm dt}=(0,1,-4t)[/tex]

We get the point (3, 2, -12) when [tex]t=2[/tex], for which the tangent vector is

[tex]\vec T(2)=(0,1,-8)[/tex]

Then the line tangent to the parabola at [tex]t=2[/tex] passing through the point (3, 2, -12) has vector equation

[tex]\ell(t)=(3,2,-12)+t(0,1,-8)=(3,2+t,-12-8t)[/tex]

which in parametric form is

[tex]\begin{cases}x(t)=3\\y(t)=2+t\\z(t)=-12-8t\end{cases}[/tex]

for [tex]t\in\Bbb R[/tex].

The parametric equation of the tangent line is [tex]L(t)=(3,2+t,-12-8t)[/tex]

The equation of Paraboloid is,

                 [tex]z =8-x-x^{2} -2y^{2}[/tex]

Equation of parabola when [tex]x = 3[/tex] is,

       [tex]z=8-3-3^{2} -2y^{2} \\\\z=-4-2y^{2}[/tex]

The parametric equation of parabola will be,

     [tex]r(t)=(3,t,-4-2t^{2} )[/tex]

Now, we have to find Tangent vector to this parabola is,

    [tex]T(t)=\frac{dr(t)}{dt}=(0,1,-4t)[/tex]

We get, the point [tex](3, 2, -12)[/tex] when [tex]t=2[/tex]

The tangent vector will be,

 [tex]T(2)=(0,1,-8)[/tex]

So that, the tangent line to this parabola at the point (3, 2, −12) will be,

     [tex]L(t)=(3,2,-12)+t(0,1,-8)\\\\L(t)=(3,2+t,-12-8t)[/tex]

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Answer:

a) [tex]P(X=16)=(16C16)(0.7)^{16} (1-0.7)^{16-16}=0.00332[/tex]

b) [tex]P(X<10) = 1-P(X\geq 10) = 1- [P(X=10)+P(X=11)+P(X=12)+P(X=13)+P(X=14)+P(X=15)+P(X=16)][/tex]

And we can find the individual probabilities like this:

[tex]P(X=10)=(16C10)(0.7)^{10} (1-0.7)^{16-10}=0.1649[/tex]

[tex]P(X=11)=(16C11)(0.7)^{11} (1-0.7)^{16-11}=0.2099[/tex]

[tex]P(X=12)=(16C12)(0.7)^{12} (1-0.7)^{16-12}=0.2040[/tex]

[tex]P(X=13)=(16C13)(0.7)^{13} (1-0.7)^{16-13}=0.1465[/tex]

[tex]P(X=14)=(16C14)(0.7)^{14} (1-0.7)^{16-14}=0.0732[/tex]

[tex]P(X=15)=(16C15)(0.7)^{15} (1-0.7)^{16-15}=0.0228[/tex]

[tex]P(X=16)=(16C16)(0.7)^{16} (1-0.7)^{16-16}=0.0033[/tex]

And replacing we got:

[tex]P(X<10) = 1-P(X\geq 10) = 1- [P(X=10)+P(X=11)+P(X=12)+P(X=13)+P(X=14)+P(X=15)+P(X=16)] = 1-0.825=0.175 [/tex]

c) [tex] P(x \geq 10) = P(X=10)+P(X=11)+P(X=12)+P(X=13)+P(X=14)+P(X=15)+P(X=16)[/tex]

And replacing we got 0.825

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

[tex]X \sim Binom(n=17, p=0.7)[/tex]

The probability mass function for the Binomial distribution is given as:

[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]

Where (nCx) means combinatory and it's given by this formula:

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]

Part a

And we want to find this probability:

[tex]P(X=16)=(16C16)(0.7)^{16} (1-0.7)^{16-16}=0.00332[/tex]

Part b fewer than 10 will check bags

We want this probability:

[tex] P(X<10) [/tex]

We can use the complement rule and we have:

[tex]P(X<10) = 1-P(X\geq 10) = 1- [P(X=10)+P(X=11)+P(X=12)+P(X=13)+P(X=14)+P(X=15)+P(X=16)][/tex]

And we can find the individual probabilities like this:

[tex]P(X=10)=(16C10)(0.7)^{10} (1-0.7)^{16-10}=0.1649[/tex]

[tex]P(X=11)=(16C11)(0.7)^{11} (1-0.7)^{16-11}=0.2099[/tex]

[tex]P(X=12)=(16C12)(0.7)^{12} (1-0.7)^{16-12}=0.2040[/tex]

[tex]P(X=13)=(16C13)(0.7)^{13} (1-0.7)^{16-13}=0.1465[/tex]

[tex]P(X=14)=(16C14)(0.7)^{14} (1-0.7)^{16-14}=0.0732[/tex]

[tex]P(X=15)=(16C15)(0.7)^{15} (1-0.7)^{16-15}=0.0228[/tex]

[tex]P(X=16)=(16C16)(0.7)^{16} (1-0.7)^{16-16}=0.0033[/tex]

And replacing we got:

[tex]P(X<10) = 1-P(X\geq 10) = 1- [P(X=10)+P(X=11)+P(X=12)+P(X=13)+P(X=14)+P(X=15)+P(X=16)] = 1-0.825=0.175 [/tex]

Part c at least 10 bags

We can find this probability like this:

[tex] P(x \geq 10) = P(X=10)+P(X=11)+P(X=12)+P(X=13)+P(X=14)+P(X=15)+P(X=16)[/tex]

And replacing we got 0.825

The probability that all 16 passengers will check their bags given a 70% chance for each passenger is found using a binomial distribution, resulting in a probability of 0.0047 when rounded to four decimal places.

The question involves calculating the probability of passengers checking bags in a binomial distribution context. Since each passenger is an independent trial and has a 70 percent chance or probability (p=0.70) of checking bags, this indeed constitutes a binomial problem. Here, success is defined as a passenger checking their bags.

To find the probability that all 16 passengers will check their bags, we need to consider the binomial probability formula for exactly 'k' successes in 'n' trials: P(X = k) = (n choose k) * p^k * (1-p)^(n-k). For this case, every passenger checks their bags, meaning 'k' is 16 and 'n' is also 16.

The formula simplifies in this scenario to P(X = 16) = 0.70^16, as the combination of 16 choose 16 is 1. Following the calculation:

P(X = 16) = 0.70^16 = 0.0047 (rounded to four decimal places).

Answer:

The driving distance for meeting at the three centres can be written as

d1=columbus

d2=Des moines

d3=Boise

The distance from des moines to columbus to 650 miles

from Boise to des moines is 1350

Therefore the distance from columbus to Boise

if the meeting is holding at columbus

0+650+1350=2000

Pr(columbus)=1/3

Pr(Des moines)=1/3

Pr(Boise)=1/3

a. Probability distribution is

capital       c            DM         B

di               0            650        2000

Pr(di)           1/3           1/3         1/3

b. Expected value is multiplication of the probability of d1 and the outcome

E(x)=0*1/3=0

c. find the variance of d1 first

Var=(x-E(x))^2*Pr(d1)

Var=(0-0)^2*1/3

Var=0

the square root of var=standard deviation

S.D=0

d. probability distribution of d2 and d3 is equal to the probability distribution of d1 , because they all have a probability of 1/3(the likelihood that an event will occur is 1/3 for the meeting \location

e. d1=0

d2=650

d1+d2=650

pr(d1+d2)=1/3+1/3=2/3

Pr(d1+d2) will be on the vertical axis, while d1+d2 will be plotted on the horizontal axis of the probability distribution graph

Step-by-step explanation:

The driving distance for meeting at the three centres can be written as

d1=columbus

d2=Des moines

d3=Boise

The distance from des moines to columbus to 650 miles

from Boise to des moines is 1350

Therefore the distance from columbus to Boise

if the meeting is holding at columbus

0+650+1350=2000

Pr(columbus)=1/3

Pr(Des moines)=1/3

Pr(Boise)=1/3

a. Probability distribution is

capital       c            DM         B

di               0            650        2000

Pr(di)           1/3           1/3         1/3

b. Expected value is multiplication of the probability of d1 and the outcome

E(x)=0*1/3=0

c. find the variance of d1 first

Var=(x-E(x))^2*Pr(d1)

Var=(0-0)^2*1/3

Var=0

the square root of var=standard deviation

S.D=0

d. probability distribution of d2 and d3 is equal to the probability distribution of d1 , because they all have a probability of 1/3(the likelihood that an event will occur is 1/3 for the meeting \location

e. d1=0

d2=650

d1+d2=650

pr(d1+d2)=1/3+1/3=2/3

Pr(d1+d2) will be on the vertical axis, while d1+d2 will be plotted on the horizontal axis of the probability distribution graph

Answer:

5

Step-by-step explanation:

numerator degrees of freedom=[tex]Treatments-1[/tex]

[tex]N_d_f=5-1=4[/tex]

Total degrees of freedom=[tex]Treatments\times \ Observations Recorded-1[/tex]

[tex]T_d_f=5\times13-1=64[/tex]

Denominator Degrees of freedom=[tex]T_d_f-N_d_f=64-4=60[/tex]

Therefore, to calculate the degrees of freedom corressponding to treatments:

[tex]F=\frac{MSR}{MSE}\\MSR=200\div4=50\\MSE=(800-200)\div 60=10\\F=50\div10=5[/tex]

Answer:

A) P(A⋂B) = 0.35

B) P(A⋃B)= 0.53

C) P(A⋂B′) = 0.08

D) P(A|B) = 0.778

Step-by-step explanation:

We know the following from the question:

- Let Proportion of Americans who expect to save more money next year than they saved last year be

P(A) and its = 0.43

-Let proportion who plan to reduce debt next year be P(B) and it's =0.81

A) probability that this person expects to save more money next year and plans to reduce debt next year which is; P(A⋂B) = 0.43 x 0.81 = 0.348 approximately 0.35

B) probability that this person expects to save more money next year or plans to reduce debt next year which is;

P(A⋃B)= P(A) + P(B) − P(A⋂B)

So, P(A⋃B)= 0.43 + 0.45 − 0.35 = 0.53

C). Probability that this person expects to save more money next year and does not plan to reduce debt next year which is;

P(A⋂B′) = P(A) − P(A⋂B)

P(A⋂B′) =0.43 − 0.35 = 0.08

D) Probability that this person does not expect to save more money given that he/she does plan to reduce debt next year which is;

P(A|B) = [P(A⋂B)] / P(B)

So P(A|B) =0.35/0.45 = 0.778

The probabilities for the given scenarios are as follows: a. 34.93%, b. 53.07%, c. 8.07%, and d. 126.67%.

a. To find the probability that a person expects to save more money next year and plans to reduce debt next year, we need to multiply the probabilities of both events occurring. The probability that a person expects to save more money next year is 43%, and of those who expect to save more money next year, 81% plan to reduce debt. Therefore, the probability is 0.43  imes 0.81 = 0.3493, or 34.93%.

b. To find the probability that a person expects to save more money next year or plans to reduce debt next year, we can add the probabilities of both events occurring and subtract the probability of both events occurring at the same time (found in part a). The probability of expecting to save more money next year is 43%, and the probability of planning to reduce debt next year is 45%. Therefore, the probability is 0.43 + 0.45 - 0.3493 = 0.5307, or 53.07%.

c. To find the probability that a person expects to save more money next year and does not plan to reduce debt next year, we subtract the probability from part a from the probability of expecting to save more money next year. The probability of expecting to save more money next year is 43%, and the probability of both expecting to save more money and planning to reduce debt is 34.93%. Therefore, the probability is 0.43 - 0.3493 = 0.0807, or 8.07%.

d. To find the probability that a person does not expect to save more money given that he/she does plan to reduce debt next year, we need to divide the probability of not expecting to save more money by the probability of planning to reduce debt next year. The probability of not expecting to save more money is 1 - 0.43 = 0.57, and the probability of planning to reduce debt next year is 45%. Therefore, the probability is 0.57 / 0.45 = 1.2667, or 126.67%.

https://brainly.com/question/35203949

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Answer:

0.0904 or 9.04%

Step-by-step explanation:

Mean glucose (μ) = 93.5

Standard deviation (σ) = 19.8

In a normal distribution, the z-score for any glucose value, X, is given by:

[tex]Z= \frac{X-\mu}{\sigma}[/tex]

For X = 120, the z-score is:

[tex]Z= \frac{120-93.5}{19.8}\\ Z=1.3384[/tex]

A z-score of 1.3384 corresponds to the 90.96th percentile of a normal distribution. Therefore, the probability that glucose exceeds 120 in this population is:

[tex]P(X>120) = 1-0.9096=0.0904 = 9.04\%[/tex]

Answer:

Probability that glucose exceeds 120 in this population is 0.09012.

Step-by-step explanation:

We are given that in a population of adults between the ages of 18 and 49, glucose follows a normal distribution with a mean of 93.5 and standard deviation of 19.8, i.e.; [tex]\mu[/tex] = 93.5  and  [tex]\sigma[/tex] = 19.8 .

Let X = amount of glucose i.e. X ~ N([tex]\mu = 93.5 , \sigma^{2} = 19.8^{2}[/tex])

Now, the Z score probability is given by;

           Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)

So,Probability that glucose exceeds 120 in this population =P(X>120)

P(X > 120) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{120-93.5}{19.8}[/tex] ) = P(Z > 1.34) = 1 - P(Z <= 1.34)

                                                   = 1 - 0.90988 = 0.09012 .

Answer:

Yes, Tom must be admitted to this university.

Step-by-step explanation:

We are given that the scores on national test are normally distributed with a mean of 500 and a standard deviation of 100.

Also, we are provided with the condition that Tom wants to be admitted to this university and he knows that he must score better than at least 70% of the students who took the test.

Let, X = score in national test, so X ~ N([tex]\mu=500 , \sigma^{2} = 100^{2}[/tex])

The standard normal z distribution is given by;

              Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)

Now, z score of probability that tom scores 585 is;

             Z = [tex]\frac{585-500}{100}[/tex] = 0.85

Now, proportion of students scoring below 85% marks is given by;

P(Z < 0.85) = 0.80234

This shows that Tom scored 80.23% of the students who took test while he just have to score more than 70%.

So, it means that Tom must be admitted to this university.

Answer:

Mean = 94

Standard deviation = 1.12

The sampling distribution of the sample mean is going to be normally distributed, beause the size of the samples are 80, which is larger than 30.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sample means with size n of at least 30 can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation, which is also called standard error [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

In this problem, we have that:

[tex]\mu = 94, \sigma = 10[/tex]

By the Central Limit Theorem

The sampling distribution of the sample mean is going to be normally distributed, beause the size of the samples are 80, which is larger than 30.

Mean = 94

Standard deviation:

[tex]s = \frac{10}{\sqrt{80}} = 1.12[/tex]

Answer:

The sequence {an} is A. unbounded

Step-by-step explanation:

The sequence {an} is unbounded.

we say a sequence is bounded if and only it is bounded both above and it is also bounded below. clearly the sequence {an} is an unbounded sequence.

The sequence {an} is bounded if there is a number M>0 such that |an|≤M for every positive n.Every unbounded sequence is divergent

The sequence{an}. is an unbounded sequence, because it has no a finite upper bound