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Suppose a simple random sample of size n= 125 is obtained from a population whose size is N= 25,000 and whose population proportion with a specified characteristic is p = 0.8. Complete parts (a) through (c) below. (a) Describe the sampling distribution of p. Choose the phrase that best describes the shape of the sampling distribution below. O A. Approximately normal because ns0.05N and np(1 - p) 2 10. O B. Approximately normal because ns0.05N and np(1 - p) < 10. O C. Not normal because ns0.05N and np(1-p)< 10. O D. Not normal becausens0.05N and np(1 -p) 2 10. Determine the mean of the sampling distribution of p. HA = (Round to one decimal place as needed.)

Suppose a simple random sample of size n= 125 is obtained from a population whose size is N= 25,000 and whose population proportion with a specified characteristic is p = 0.8. Complete parts (a) through (c) below. (a) Describe the sampling distribution of p. Choose the phrase that best describes the shape of the sampling distribution below. O A. Approximately normal because ns0.05N and np(1 - p) 2 10. O B. Approximately normal because ns0.05N and np(1 - p) < 10. O C. Not normal because ns0.05N and np(1-p)< 10. O D. Not normal becausens0.05N and np(1 -p) 2 10. Determine the mean of the sampling distribution of p. HA = (Round to one decimal place as needed.)

MATLAB: An Introduction with Applications
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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Suppose a simple random sample of size \( n = 125 \) is obtained from a population whose size is \( N = 25,000 \) and whose population proportion with a specified characteristic is \( p = 0.8 \). Complete parts (a) through (c) below. --- **(a) Describe the sampling distribution of \(\hat{p}\).** Choose the phrase that best describes the shape of the sampling distribution below. - **A.** Approximately normal because \( n \leq 0.05N \) and \( np(1-p) \geq 10 \). - **B.** Approximately normal because \( n \leq 0.05N \) and \( np(1-p) < 10 \). - **C.** Not normal because \( n \leq 0.05N \) and \( np(1-p) < 10 \). - **D.** Not normal because \( n \leq 0.05N \) and \( np(1-p) \geq 10 \). **Determine the mean of the sampling distribution of \(\hat{p}\).** \[ \mu_{\hat{p}} = \_\_\_ \] (Round to one decimal place as needed.) **Determine the standard deviation of the sampling distribution of \(\hat{p}\).** \[ \sigma_{\hat{p}} = \_\_\_ \] (Round to six decimal places as needed.)
Transcribed Image Text:Suppose a simple random sample of size \( n = 125 \) is obtained from a population whose size is \( N = 25,000 \) and whose population proportion with a specified characteristic is \( p = 0.8 \). Complete parts (a) through (c) below. --- **(a) Describe the sampling distribution of \(\hat{p}\).** Choose the phrase that best describes the shape of the sampling distribution below. - **A.** Approximately normal because \( n \leq 0.05N \) and \( np(1-p) \geq 10 \). - **B.** Approximately normal because \( n \leq 0.05N \) and \( np(1-p) < 10 \). - **C.** Not normal because \( n \leq 0.05N \) and \( np(1-p) < 10 \). - **D.** Not normal because \( n \leq 0.05N \) and \( np(1-p) \geq 10 \). **Determine the mean of the sampling distribution of \(\hat{p}\).** \[ \mu_{\hat{p}} = \_\_\_ \] (Round to one decimal place as needed.) **Determine the standard deviation of the sampling distribution of \(\hat{p}\).** \[ \sigma_{\hat{p}} = \_\_\_ \] (Round to six decimal places as needed.)
**Determine the standard deviation of the sampling distribution of \(\hat{p}\).** \[ \sigma_{\hat{p}} = \ [\text{Round to six decimal places as needed.}] \] **(b) What is the probability of obtaining \(x = 105\) or more individuals with the characteristic? That is, what is \(P(\hat{p} \geq 0.84)\)?** \[ P(\hat{p} \geq 0.84) = \ [\text{Round to four decimal places as needed.}] \] **(c) What is the probability of obtaining \(x = 90\) or fewer individuals with the characteristic? That is, what is \(P(\hat{p} \leq 0.72)\)?** \[ P(\hat{p} \leq 0.72) = \ [\text{Round to four decimal places as needed.}] \]
Transcribed Image Text:**Determine the standard deviation of the sampling distribution of \(\hat{p}\).** \[ \sigma_{\hat{p}} = \ [\text{Round to six decimal places as needed.}] \] **(b) What is the probability of obtaining \(x = 105\) or more individuals with the characteristic? That is, what is \(P(\hat{p} \geq 0.84)\)?** \[ P(\hat{p} \geq 0.84) = \ [\text{Round to four decimal places as needed.}] \] **(c) What is the probability of obtaining \(x = 90\) or fewer individuals with the characteristic? That is, what is \(P(\hat{p} \leq 0.72)\)?** \[ P(\hat{p} \leq 0.72) = \ [\text{Round to four decimal places as needed.}] \]
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