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Suppose a simple random sample of size $n=75$ is obtained from a population whose size is $N=30,000$ and whose population proportion with a specified characteristic is $p=0.6$. Complete parts (a) through (c) below. (a) Describe the sampling distribution of $p^ $. Choose the phrase that best describes the shape of the sampling distribution below. A. Approximately normal because $n≤0.05N$ and $np(1−p)<10$. B. Not 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 $p^ $. $pμ_{p^} =$ (Round to one decimal place as needed.) Determine the standard deviation of the sampling distribution of $p^ $. $σ_{p^}=$ (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 $P(p^ ≥0.68)$ ? $P(p^ ≥0.68)=$ (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 $P(p^ ≤0.48)$ ? $P(p^ ≤0.48)=(Round to four decimal places as needed.)$

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