Question

Suppose a simple random sample of size $n=1460$ is obtained from a population whose size is $N=1,500,000$ and whose population proportion with a specified characteristic is $p=0.42$ (a) Describe the sampling distribution of $\hat{p}$ (b) What is the probability of obtaining $x=657$ or more individuals with the characteristic? (c) What is the probability of obtaining $x=584$ or fewer individuals with the characteristic?

          Suppose a simple random sample of size $n=1460$ is obtained from a population whose size is $N=1,500,000$ and whose population proportion with a specified characteristic is $p=0.42$
(a) Describe the sampling distribution of $\hat{p}$
(b) What is the probability of obtaining $x=657$ or more individuals with the characteristic?
(c) What is the probability of obtaining $x=584$ or fewer individuals with the characteristic?

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Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Ivan Kochetkov

07/14/2023

Step 1

42$ and standard deviation $\sigma_{\hat{p}}=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.42(1-0.42)}{1460}}\approx 0.025$. (b) Show more…

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Suppose a simple random sample of size $n=1460$ is obtained from a population whose size is $N=1,500,000$ and whose population proportion with a specified characteristic is $p=0.42$ (a) Describe the sampling distribution of $\hat{p}$ (b) What is the probability of obtaining $x=657$ or more individuals with the characteristic? (c) What is the probability of obtaining $x=584$ or fewer individuals with the characteristic?

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