(Solved): Suppose a simple random sample of size n=75 is obtained from a population whose size is N=30,000 an ...

Suppose a simple random sample of size $n=75$ is obtained from a population whose size is $\mathrm{N}=30,000$ and whose population proportion with a specified characteristic is $p=0.6$. 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 $n\le 0.05\mathrm{N}$ and $np(1-p)<10$. B. Not normal because $n\le 0.05\mathrm{N}$ and $np(1-p)<10$. C. Not normal because $n\le 0.05\mathrm{N}$ and $np(1-p)\ge 10$. D. Approximately normal because $n\le 0.05\mathrm{N}$ and $np(1-p)\ge 10$. Determine the mean of the sampling distribution of $\hat{p}$. $\underset{p}{{\mu }_{\hat{p}}}=$ (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 $x=51$ or more individuals with the characteristic? That is, what is $P(\hat{p}\ge 0.68)$ ? $P(\hat{p}\ge 0.68)=$ (Round to four decimal places as needed.) (c) What is the probability of obtaining $x=36$ or fewer individuals with the characteristic? That is, what is $P(\hat{p}\le 0.48)$ ? $P(\hat{p}\le 0.48)=\text{ (Round to four decimal places as needed.) }$