Suppose a simple random sample of size \( n = 200 \) is obtained from a population whose size is \( N = 20,000 \) and whose population proportion with a specified characteristic is \( p = 0.4 \). Complete parts (a) through (c) below.**Options:**- A. Approximately normal because \( n \leq 0.05N \) and \( np(1 - p) \geq 10 \).- B. Not normal because \( n > 0.05N \) and \( np(1 - p) \geq 10 \).- C. Not normal because \( n \leq 0.05N \) and \( np(1 - p) < 10 \).- D. Approximately normal because \( n > 0.05N \) and \( np(1 - p) \geq 10 \).**Determine the mean of the sampling distribution of \( \hat{p} \):**\[\mu_{\hat{p}} = p = 0.4 \quad \text{(Round to one decimal place as needed.)}\]**Determine the standard deviation of the sampling distribution of \( \hat{p} \):**\[\sigma_{\hat{p}} = 0.034641 \quad \text{(Round to six decimal places as needed.)}\]**(b) What is the probability of obtaining \( x = 90 \) or more individuals with the characteristic? That is, what is \( P(\hat{p} \geq 0.45) \)?**\[P(\hat{p} \geq 0.45) = 0.0745 \quad \text{(Round to four decimal places as needed.)}\]**(c) What is the probability of obtaining \( x = 66 \) or fewer individuals with the characteristic? That is, what is \( P(\hat{p} \leq 0.33) \)?**\[P(\hat{p} \leq 0.33) = 0.0918 \quad \text{(Round to four decimal places as needed.)}\]

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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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Suppose a simple random sample of size n = 200 is obtained from a population whose size is N=20,000 and whose population proportion with a specified characteristic is p=0.8. Complete parts (a) through (c) below. A. Approximately normal Decause ns. and per-p) 1. OB. Not normal because n ≤0.05N and np(1-p) 0.81)? P(p≥ 0.81)= 3632 (Round to four decimal places as needed.) (c) What is the probability of obtaining x= 150 or fewer individuals with the characteristic? That is, what is P(p ≤ 0.75)? P(p ≤ 0.75)= (Round to four decimal places as needed.) + example Get more help. alues % 5 A + 6 MacBook Pro & 7 * 00 8 Vi I, Clear all ( 9 More Check answer X
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