Defective rate can be expected
to keep an eye on a Poisson distribution. Mean is equal to 800(0.02) = 16,
Variance is 16, and so standard deviation is 4.
X = 800(0.04) = 32, Using normal approximation of the Poisson distribution Z1 =
(32-16)/4 = 4.
P(greater than 4%) = P(Z>4) = 1 – 0.999968 = 0.000032, which implies that
having such a defective rate is extremely unlikely.
If the defective rate in the random sample is 4 percent then it is very likely that the assembly line produces more than 2% defective rate now.
The probability that the defective rate exceeds 4% in the sample is approximately 0.0006, indicating a significant deviation from the expected 2%.
To solve this problem, we need to use the concept of binomial distribution and the normal approximation to the binomial distribution due to the large sample size.
Step 1: Understanding the problem
- The assembly line historically has a defective rate of 2%.
- A random sample of 800 components is drawn.
- We are interested in the probability that the defective rate is greater than 4%.
Step 2: Calculate the parameters
- Population defective rate (historical rate): [tex]\( p = 0.02 \)[/tex]
- Sample size: [tex]\( n = 800 \)[/tex]
- Sample defective rate (given): [tex]\( \hat{p} = 0.04 \)[/tex]
Step 3: Probability that defective rate is greater than 4%
- We need to find [tex]\( P(\hat{p} > 0.04) \).[/tex]
Since [tex]\( \hat{p} \)[/tex] is approximately normally distributed (by the Central Limit Theorem because [tex]\( n \)[/tex] is large), we can use the normal approximation to the binomial distribution.
Step 4: Calculate standard error of sample proportion
The standard error of the sample proportion [tex]\( \hat{p} \)[/tex] is given by:
[tex]\[ SE(\hat{p}) = \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} \][/tex]
Substitute the values:
[tex]\[ SE(\hat{p}) = \sqrt{\frac{0.04 \cdot 0.96}{800}} \][/tex]
[tex]\[ SE(\hat{p}) = \sqrt{\frac{0.0384}{800}} \][/tex]
[tex]\[ SE(\hat{p}) \approx 0.0062 \][/tex]
Step 5: Z-score calculation
To find the Z-score for [tex]\( \hat{p} = 0.04 \)[/tex]:
[tex]\[ Z = \frac{\hat{p} - p}{SE(\hat{p})} \][/tex]
[tex]\[ Z = \frac{0.04 - 0.02}{0.0062} \][/tex]
[tex]\[ Z \approx 3.23 \][/tex]
Step 6: Find the probability
Now, find the probability that [tex]\( \hat{p} > 0.04 \)[/tex]:
[tex]\[ P(\hat{p} > 0.04) = P(Z > 3.23) \][/tex]
Using the standard normal distribution table or a calculator:
[tex]\[ P(Z > 3.23) \approx 0.0006 \][/tex]
Conclusion:
The probability that the defective rate in the sample is greater than 4% is approximately [tex]\( 0.0006 \)[/tex], or [tex]\( 0.06\% \)[/tex].
Interpretation:
Since the probability is very low, it suggests that a defective rate of 4% in the sample is highly unlikely to occur if the true defective rate on the assembly line is 2%. This could indicate a potential issue or change in the process affecting the defective rate, warranting further investigation or quality control measures.
0.5 is what type of number
Answer:
Rational.
Step-by-step explanation:
We are asked to determine the type of number 0.5.
We can see that our given number is a decimal.
We can also see that our given number is a terminating decimal, so we can represent it as a fraction.
[tex]0.5\times \frac{10}{10}=\frac{5}{10}=\frac{1}{2}[/tex]
Therefor, our given number is a rational number as we can represent it as a fraction.
What is the slope of a line that is perpendicular to a line whose equation is 5y=10+2x ?
The slope of a line perpendicular to the given line is -5/2.
Explanation:The equation of the line given is 5y = 10 + 2x. To find the slope of this line, we need to rearrange the equation into the slope-intercept form, y = mx + b, where m represents the slope. Dividing both sides of the equation by 5, we get y = 2/5x + 2. Comparing this equation to the slope-intercept form, we can see that the slope is 2/5.
To find the slope of a line perpendicular to this line, we use the fact that the product of the slopes of two perpendicular lines is -1. Therefore, the slope of the perpendicular line is the negative reciprocal of the slope of the given line. The negative reciprocal of 2/5 is -5/2.
Therefore, the slope of a line that is perpendicular to the line with the equation 5y = 10 + 2x is -5/2.
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The ratio of red to greens was 5 to 16 and six times the number of reds exceeded the number of greens by 112. How many were red and how many were green?
what is bed? because I need help I don't know what the answer is
62 +62 = 124
360 - 124 = 176
176/2 = 88
BED = 88 degrees
Suppose you are trying to estimate the number of field mice in a small field. one day you capture 100 mice, mark them and release them. the next day you capture 150 mice of which 15 are marked. what is the estimate for the population size?
Sketch a triangle that has acute angle θ. cot(θ) = 2
To sketch a triangle with an acute angle θ and cot(θ) = 2, we can choose an angle in the first quadrant, such as 30 degrees, and draw a right triangle with sides 2 and 1. The hypotenuse can be found using the Pythagorean theorem.
Explanation:To sketch a triangle with an acute angle θ and cot(θ) = 2, we can use the fact that cotangent is the reciprocal of the tangent function, so tan(θ) = 1/2. Since tangents are positive in the first and third quadrants, we can consider an angle in the first quadrant. Let's choose the angle as 30 degrees.
Now, we can draw a right triangle with one of the acute angles as 30 degrees. Since tan(θ) = opposite/adjacent, we can choose the side opposite the angle as 1 and the side adjacent as 2. Therefore, the triangle has sides 2, 1, and the hypotenuse can be found using the Pythagorean theorem.
The triangle has an acute angle θ and cot(θ) = 2. It has sides of length 2, and 1, and the hypotenuse can be found using the Pythagorean theorem.
Although the actual amount varies by season and time of day, the average volume of water that flows over the falls each second is 4.84.8 times ×10 Superscript 5105 gallons. How much water flows over the falls in an hour? Write the result in scientific notation. (Hint: 1 hour equals 3600 seconds)
Belts cost $160 per carton, and shoes cost $465 per carton. If an order comes in for a total of 88 cartons for $19,265, what is the number of cartons of belts?
Find k so that the line containing the points (-5,k) and (2,10) is parallel to the line containing the points (5,5) and (1,-4)
Final answer:
To find the value of k so that the line containing the points (-5,k) and (2,10) is parallel to the line containing the points (5,5) and (1,-4), we need to find the slope of the second line and use it to find the value of k.
Explanation:
To find the value of k so that the line containing the points (-5, k) and (2, 10) is parallel to the line containing the points (5, 5) and (1, -4), we need to find the slope of the second line and use it to find the value of k. Firstly, let's find the slope of the second line:
The formula we apply is the slope
= (y2 - y1) / (x2 - x1).
slope = -9 / -4 = 9/4;
slope = (-4 - 5) / (1 - 5)
The lines now have the same slope since they are parallel.
So, the slope of the line passing through (-5, k) and (2, 10) should also be 9/4. We can find the slope using the formula:
slope = (y2 - y1) / (x2 - x1)
Substituting the coordinates (-5, k) and (2, 10):
9/4 = (10 - k) / (2 - (-5))
By simplifying the equation, we get:
9 = 7(10 - k)
Now, let's solve for k:
90 - 9k = 63
-9k = 63 - 90
-9k = -27
k = 3
One number is 4 less than a second number. Twice the second number is 16 less than 5 times the first. Find the two numbers.
The two numbers are 8 and 12.
What is Algebraic expression ?
Algebraic expressions are numbers expressed using letters or alphabets without specifying their values. Algebra taught us how to express unknown values using letters such as x, y, and z. There can also be a single value that is placed before and multiplied by a variable in an algebraic expression in addition to these letters, which are called variables.
Let us assume first number be = x
and, let the second number be = y
the,
One number is 4 less than a second number means :
x = y - 4........(1)
Twice the second number is 16 less than 5 times the first means :
2y = 5x - 16.......(2)
Substitute x equals from the first equation in the second equation.
2y = 5(y - 4) - 16
2y = 5y - 20 - 16
-3y = -36
y = 12
Now use the first equation for find x.
x = y - 4
x = 12 - 4
x = 8
Thus, The numbers are 8 and 12.
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If the assessed valuation is $103,220 and the tax rate per $100 is $4.32, what is the annual tax?
A) $3,924.45
B) $3,565.24
C) $3,058.08
D) $4,459.10
I got D, is that correct?
An instructor has given a short quiz consisting of two parts. for a randomly selected student, let x = the number of points earned on the first part and y = the number of points earned on the second part. suppose that the joint pmf of x and y is given in the accompanying table. y p(x, y) 0 5 10 15 x 0 0.02 0.06 0.02 0.10 5 0.04 0.13 0.20 0.10 10 0.01 0.15 0.16 0.01 (a) if the score recorded in the grade book is the total number of points earned on the two parts, what is the expected recorded score e(x + y)? (enter your answer to one decimal place.) (b) if the maximum of the two scores is recorded, what is the expected recorded score? (enter your answer to two decimal places.)
The expected recorded score when the total number of points earned on the two parts is recorded is 20.4.
The expected recorded score when the maximum of the two scores is recorded is 25.7.
We have,
(a)
If the score recorded in the grade book is the total number of points earned on the two parts (x + y):
We will calculate the expected value (E) using the joint probability mass function (pmf) values given in the table.
E(x + y) = Σ[(x + y) * p(x, y)]
Using the table values:
E(x + y) = (0 * 0.02) + (5 * 0.06) + (10 * 0.02) + (15 * 0.10) + (20 * 0.04) + (25 * 0.13) + (30 * 0.20) + (35 * 0.10) + (40 * 0.01) + (45 * 0.15) + (50 * 0.16) + (55 * 0.01)
E(x + y) = 20.4
(b)
If the maximum of the two scores is recorded:
We need to find the maximum value between x and y for each combination of scores in the table and calculate the expected value using the joint pmf.
E(max(x, y)) = Σ[max(x, y) * p(x, y)]
Using the table values:
E(max(x, y)) = (0 * 0.02) + (5 * 0.06) + (10 * 0.15) + (15 * 0.20) + (20 * 0.20) + (25 * 0.15) + (30 * 0.15) + (35 * 0.15) + (40 * 0.16) + (45 * 0.16) + (50 * 0.16) + (55 * 0.01)
E(max(x, y)) = 25.7
Therefore,
The expected recorded score when the total number of points earned on the two parts is recorded is 20.4.
The expected recorded score when the maximum of the two scores is recorded is 25.7.
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The expected recorded score in the grade book (E(X+Y)) is calculated by multiplying each possible total score by its probability and summing these products. The expected maximum score is calculated similarly, but considers the probabilities of each possible maximum score. Application of these principles requires access to full probability mass function data.
Explanation:The student's question relates to the calculation of expected values in the context of a two-part quiz, with scores registered as the total (x+y) or the maximum of the two scores. Given a joint probability mass function (pmf) for x and y, we can calculate expected scores in both cases.
Generally, the expected value E(X) of a discrete random variable X is calculated by multiplying each possible value of X by its probability, and then summing these products. This is represented by the formula E(X) = Σ xP(x). Assuming the same logic for the expected total score on the quiz, E(X+Y) would be calculated by summing the products of each possible total score and its probability.
To find the expected maximum score, we'd perform a similar calculation, but consider the probabilities of each possible maximum score instead.
Without explicit probabilities in the question, no exact solutions can be provided. However, the processes outlined here would allow the student to solve such problems with access to the full pmf data.
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Given the following set of data, which measures have a value of 6? (Check all that apply.)
3, 4, 6, 8, 9
A.range
B.mode
C.median
D.mean
what is (4+49)-4x10=
Sometimes integers are encoded by using four-digit binary expansions to represent each decimal digit. this produces the binary coded decimal form of the integer. for instance, 791 is encoded in this way by 011110010001. how many bits are required to represent a number with n decimal digits using this type of encoding
Which number identifies the amount of fuel remaining in the tank? cross out A. 0.312 cross out B. 0.375 cross out C. 0.550 cross out D. 0.625
Write an equation in slope intercept form for a line that goes through the points (-4,0) and (1,-5).
Which table best represents the steps to solve the equation 8 + x over 3 = 4?
i accidentaly highlighted the first one but i really need help on this and need the answer thank you! so much!
What is the value of the digit 4 in 46000?
Can some one show me how to do this pleases?!.
A customer went to a garden shop and bought some potting soil for $17.50 and 4 shrubs. The total bills was $53.50. Write and solve an equation to find the price of each shrub
66681 to the nearest ten thousand
Write 405,612 in expanded form
The earth's radius is 6.37×106m; it rotates once every 24 hours. you may want to review ( pages 195 - 198) . part a what is the earth's angular speed
The angular speed of Earth is [tex]\fbox{\begin\\\ \bf 7.268\times 10^{-5}\ \text{radian per second}\\\end{minispace}}[/tex].
Further explanation:
It is given that the radius of Earth is [tex]6.37\times10^{6}\ \text{meters}[/tex] and it rotates once in every [tex]24[/tex] hours.
The angular speed of earth is nearly constant and Earth takes one day to complete one rotation that means the time interval for earth to complete one revolution is [tex]1\ \text{day}[/tex].
The total angular displacement covered by the earth to complete one revolution is [tex]2\pi\text{radian}[/tex].
One day is equivalent to [tex]24\ \text{hours}[/tex], [tex]1\ \text{hour}[/tex] is equivalent to [tex]60\ \text{minutes}[/tex] and [tex]1\ \text{minute}[/tex] is equivalent to [tex]60\ \text{seconds}[/tex].
The total number of seconds in [tex]1\ \text{day}[/tex] is calculated as follows:
[tex]\fbox{\begin\\\ \begin{aligned}1\ \text{day}&=24\ \text{hours}\\&=24\times60\ \text{minutes}\\&=1440\ \text{minutes}\\&=1440\times60\ \text{seconds}\\&=86400\ \text{seconds}\end{aligned}\\\end{minispace}}[/tex]
Therefore the time taken to complete one revolution is [tex]86400\ \text{seconds}[/tex].
The angular velocity is defined as the rate of change of angular displacement. So the formula for angular velocity is, as follows:
[tex]\fbox{\begin\\\ \omega=\dfrac{\theta}{t}\\\end{minispace}}[/tex]
In the above equation [tex]\omega[/tex] represents angular velocity, [tex]\theta[/tex] represents angular displacement and [tex]t[/tex] represents time.
To obtain the value of angular velocity of Earth substitute [tex]2\pi[/tex] for [tex]\theta[/tex] and [tex]86400[/tex] for [tex]t[/tex] in the above equation.
[tex]\begin{aligned}\omega&=\dfrac{2\pi}{86400}\\&=\dfrac{2\times3.14}{86400}\\&=\dfrac{6.28}{86400}\\&=7.268\times10^{-5}\end{aligned}[/tex]
Therefore, the value of [tex]\omega[/tex] is [tex]7.268\times10^{-5}[/tex].
Thus, the angular speed of the Earth is [tex]\fbox{\begin\\\ \bf 7.268\times 10^{-5}\ \text{radian per second}\\\end{minispace}}[/tex].
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Grade: High school
Subject: Mathematics
Chapter: Angular motion
Keyword: Angular velocity, angular displacement, time, one revolution, radian/second, Earth, 86400 seconds, 2pi, speed, minutes, omega, theta.
Starting at sea level, a submarine descends at a constant rate to a depth of −4/5 mile relative to sea level in 3 minutes. What was the submarine's depth relative to sea level after the first minute? Enter your answer in the comments.
Which statements about limiting reactants are correct? more than one answer may be correct?
"if we have a distribution of x values that is more or less mound-shaped and somewhat symmetrical, what is the sample size n needed to claim that the distribution of sample means x from random samples of that size is approximately normal"
Explain why it works to break apart a number by place values to multiply
A black-tailed jackrabbit hops about 7 feet in a single hop how far can a hop in 5 seconds
Answer:
A black-tailed jackrabbit can hopes 36 in 5 seconds.
Step-by-step explanation:
Consider the provided information.
Black tailed jackrabbit hopes 51 feet in one second.
Therefore, in 5 second Black tailed jackrabbit covers a distance of:
51×5=255 feet
So, in 5 seconds a black-tailed jackrabbit will travel 255 feet.
In one hops Black tailed jackrabbit covers 7 feet.
Now find the number of hops, we need to divide the distance by the length of one hop:
[tex]255\div 7=\frac{255}{7}\approx36[/tex]
Hence, A black-tailed jackrabbit can hopes 36 in 5 seconds.
Imagine you have an urn containing 5 red, 3 blue, and 2 orange marbles in it. 1. what is the probability that the first marble you draw is blue?
Two factors have an estimated product of 10,000. One is a single digit. What two factors can they be. Explain your thinking