Suppose a simple random sample of size n = 50 is obtained from a population whose size is N = 10,000 and whose population proportion with a specified characteristic is p = 0.4. 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.** Not normal because n ≤ 0.05N and np(1−p) < 10.- **B.** Approximately normal because n ≤ 0.05N and np(1−p) < 10.- **C.** Not normal because n ≤ 0.05N and np(1−p) ≥ 10.- **D.** Approximately normal because n ≤ 0.05N and np(1−p) ≥ 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.)---**(b) What is the probability of obtaining x = 23 or more individuals with the characteristic?** That is, what is \( P(\hat{p} ≥ 0.46) \)?\[ P(\hat{p} ≥ 0.46) = \, \_\_\_ \] (Round to four decimal places as needed.)---**(c) What is the probability of obtaining x = 18 or fewer individuals with the characteristic?** That is, what is \( P(\hat{p} ≤ 0.36) \)?\[ P(\hat{p} ≤ 0.36) = \, \_\_\_ \] (Round to four decimal places as needed.)

We want to find mean and standard deviation and following probability

Answered: Suppose a simple random sample of size…

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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