**Text Transcription:**A machine that manufactures automobile pistons is estimated to produce a defective piston 3% of the time. Suppose that this estimate is correct and that a random sample of 90 pistons produced by this machine is taken.Answer the following. (If necessary, consult a list of formulas.)(a) Estimate the number of pistons in the sample that are defective by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response.(b) Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your response to at least three decimal places.

a) Suppose a random variable X, defines that the number of defective pistons.

Answered: A machine that manufactures automobile…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The weight of a loaf of bakery bread at the grocery store follows a Normal distribution with a mean of μ = 12 ounces and a standard deviation of σ = 1 ounce. Suppose we pick four loaves at random from the bin and find their total weight, W. Which of the following statements describes the random variable W? O The random variable W is binomial, with a mean of 48 ounces and a standard deviation of two ounces. O The random variable W is binomial, with a mean of 12 ounces and a standard deviation of two ounces. O The random variable W is Normal, with a mean of 12 ounces and a standard deviation of one ounce. O The random variable W is Normal, with a mean of 48 ounces and a standard deviation of two ounces. O The random variable W is Normal, with a mean of 48 ounces and a standard deviation of four ounces.
A rainstorm in Portland, Oregon, wiped out the electricity in 5% of the households in the city. Suppose that a random sample of 80 Portland households is taken after the rainstorm. Answer the following. (If necessary, consult a list of formulas.) (a) Estimate the number of households in the sample that lost electricity by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response. (b) Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your response to at least three decimal places.
Assume x is a normally distributed random variable with mean = 50 and variance = 3. Find the value of the random variable x0 when P(x ≤ x0) = .8413 A. 33 B. 49 C. 53 D. 16
A rainstorm in Portland, Oregon, wiped out the electricity in 5% of the households in the city. Suppose that a random sample of 80 Portland households is taken after the rainstorm. Answer the following. (If necessary, consult a list of formulas.) (a) Estimate the number of households in the sample that lost electricity by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response. (b) Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your response to at least three decimal places. 2022 Graw Hill LLC All Rights acer esc 6 # @ 4 3 2 t
The accompanying table describes results from groups of 10 births from 10 different sets of parents. The random variable x represents the number of girls among 10 children. Use the range rule of thumb to determine whether 1 girl in 10 births is a significantly low number of girls. x P(x)0 0.0041 0.0132 0.0363 0.1154 0.2065 0.2386 0.2017 0.1168 0.0459 0.01310 0.013 The maximum value in this range is __ girls. (round to one decimal places as needed) The minimum value in this range is __ girls. (round to one decimal place as needed) Based on the result, is 1 girl in 10 births a significantly low number of girls? Explain. A. No, 1 girl is not a significantly low number of girls, because 1 girl is within the range of values that are not significant. B. Yes, 1 girl is a significantly low number of girls, because 1 girl is below the range of values that are not significant. C. Yes, 1 girl is a significantly low number of girls, because 1 girl is above the…
Let x be a random variable representing the starting salary of a first-year teacher in a city. A report claims that the mean starting salary of these first-year teachers is greater than $50,000. To test this claim we find that a random sample of 20 teachers has a mean starting salary of $51,425 with a sample standard deviation of $3,549. If you assume that the population mean is $50,000, find the P-value corresponding to the hypothesis that the mean starting salary of the first-year teachers is greater than $50,000.
Let x be a random variable representing the starting salary of a first-year teacher in a city. A report claims that the mean starting salary of these first-year teachers is less than $52,000. To test this claim we find that a random sample of 25 teachers has a mean starting salary of $51,875 with a sample standard deviation of $1,055. If you assume that the population mean is $52,000, find the P-value corresponding to the hypothesis that the mean starting salary of the first-year teachers is less than $52,000. A. 0.28 B. 0.56 C. 0.14 D. 0.36
A random sample of n = 100 observations is selected from a population with u = 31 and o = 21. Approximate the probabilities shown below. a. P(x2 28) c. P(xs 28.2) b. P(22.1sxs26.8) d. P(x2 27.0) Click the icon to view the table of normal curve areas.
The general philosophy of standardizing is that standardizing a random variable involves a. Subtracting the main in the batting by the standard deviation b. Dividing the standard deviation of the total of successes by the total of trials c. Adding and subtracting standard deviations in each direction d. Subtracting the area in the right tail from 1 since the Z chart gives only the area "to the left"
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Let Y = 3X – 1, where X is a random variable that is distributed uniformly from 10 to 50. Answer the following questions.a. What is the probability that X takes any value from 20 to 30? Draw the distribution and identify this probability in the distribution. Show your calculations.b. Calculate the expected value of X in addition to the variance and standard deviation of X. Show your calculations.c. Calculate the expected value of Y in addition to the variance and standard deviation of Y. Show your calculations.
Determine if the finite correction factor should be used. If so, use it in your calculations when you find the probability. In a sample of 700 gas stations, the mean price for regular gasoline at the pump was $2.898 per gallon and the standard deviation was $0.008 per gallon. A random sample of size 60 is drawn from this population. What is the probability that the mean price per gallon is less than $2.897? The probability that the mean price per gallon is less than $2.897 is (Round to four decimal places as needed.)

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