Statistics Questions & Answers

Describe the sampling distribution of \( \hat{p} \). Assume the size of the population is 25,000 . \( n=1100, p=0.365 \) Describe the shape of the sampling distribution of \( \hat{p} \). Choose the correct answer below. A. The shape of the sampling distribution of \( \hat{p} \) is not normal because \( n \leq 0.05 \mathrm{~N} \) and \( n \mathrm{np}(1-\mathrm{p}) \geq 10 \). B. The shape of the sampling distribution of \( \hat{p} \) is not normal because \( n \leq 0.05 \mathrm{~N} \) and \( n p(1-p)<10 \). The shape of the sampling distribution of \( \hat{p} \) is approximately normal because \( n \leq 0.05 \mathrm{~N} \) and \( n p(1-p) \geq 10 \). D. The shape of the sampling distribution of \( \hat{p} \) is approximately normal because \( n \leq 0.05 \mathrm{~N} \) and \( \mathrm{np}(1-\mathrm{p})<10 \). Determine the mean of the sampling distribution of \( \hat{p} \). \( \mu_{\hat{p}}=\square \) (Round to three decimal places as needed.)

Describe the sampling distribution of \( \hat{p} \). Assume the size of the population is 25,000 . \( n=800, p=0.325 \) Describe the shape of the sampling distribution of \( \hat{p} \). Choose the correct answer below. A. The shape of the sampling distribution of \( \hat{p} \) is not normal because \( n \leq 0.05 \mathrm{~N} \) and \( n p(1-p)<10 \). The shape of the sampling distribution of \( \hat{p} \) is approximately normal because \( n \leq 0.05 \mathrm{~N} \) and \( n p(1-p) \geq 10 \). C. The shape of the sampling distribution of \( \hat{p} \) is not normal because \( n \leq 0.05 \mathrm{~N} \) and \( n p(1-p) \geq 10 \). Determine the mean of the sampling distribution of \( \hat{p} \). \( \mu_{p}=0.325 \) (Round to three decimal places as needed.) Determine the standard deviation of the sampling distribution of \( \hat{p} \). \( \sigma_{\hat{p}}=\square \) (Round to three decimal places as needed.)

Problem 5 ( 10 points). The height of fifth-grade students in elementary school are normally distributed with mean ( \( \mu \) ) equal to 48 inches and a standard deviation equal to 2.8 inches. How tall in inches would a fifth-grade student need to be to have a height at the \( 91^{\text {st }} \) percentile?

16 The shape of the distribution of the time required to get an oil change at a 15 -minute oil-change facility is skewed right. However, records indicate that the mean time for an oil change is 16.7 mi is 4.4 minutes. Use StatCrunch to complete parts (a) through (c). (a) To compute probabilities regarding the sample mean using the normal model, what size sample would be required? Choose the correct answer. A. The sample size needs to be less than or equal to 30 . B. Any sample size could be used. C. The sample size needs to be greater than or equal to 30 . D. The normal model cannot be used if the shape of the distribution is skewed right. (b) What is the probability that a random sample of \( n=40 \) oil changes results in a sample mean time less than 15 minutes? The probability is approximately (Round to four decimal places as needed.)

The shape of the distribution of the time required to get an oil change at a 15 -minute oil-change facility is skewed right. However, records indicate that the mean time for an oil change is 16.7 minutes, and the s is 4.4 minutes. Use Statcrunch to complete parts (a) through (c). A. The sample size needs to be less than or equal to 30 . (a) To compute probabilities regarding the sample mean using the normal model, what size sample would be required? Choose the correct answer. C. The sample size needs to be greater than or equal to 30 . D. The normal model cannot be used if the shape of the distribution is skewed right. D.

16 Suppose a simple random sample of size \( n=36 \) is obtained from a population that is skewed right with \( \mu=74 \) and \( \sigma=6 \). (a) Describe the sampling distribution of \( x \) (b) What is \( P(x>75.95) \) ? (c) What is \( P(x \leq 71.75) \) ? (d) What is \( P(734<x<76.05) \) ? A. The distribution is uniform. (a) Choose the correct description of the shape of the sampling distribution of \( \bar{x} \). C. The distribution is skewed right. D. The distribution is approximately normal. E. The shape of the distribution is uniknown.

Determine \( \mu_{x} \) and \( \sigma_{x} \) from the given parameters of the population and sample size. \( \mu=60, \sigma=5, n=33 \) \( \mu_{x}=\square \)

Determine \( \mu_{\mathrm{x}} \) and \( \sigma_{\mathrm{x}} \) from the given parameters of the population and sample size. \( \mu=73, \sigma=18, \mathrm{n}=36 \) \( \mu_{\mathrm{x}}=\prod_{-} \)

Determine \( \mu_{\mathrm{x}} \) and \( \sigma_{\mathrm{x}} \) from the given parameters of the population and sample size.

The trade volume of a stock is the number of shares traded on a given day. The data in the first accompanying table, in millions (so that 6.16 represents \( 6,160,000 \) shares traded), represent the volume of a PepsiCo stock traded for a random sample of 38 trading days in 2018. A second random sample of 38 days in 2018 resulted in the data in the second accompanying table. Complete parts (a) through (d). Click here to view the data for sample 1. Click here to view the data for sample 2. (a) Use the data from sample 1 to compute a point estimate for the population mean number of shares traded per day in 2018. A point estimate for the population mean number of PepsiCo shares traded per day in 2018 is \( \square \) million. (Round to two decimal places as needed.)