24 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 = 0.6. 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.O A. Approximately normal because ns0.05N and np(1 - p) 10.B. Not normal because n s0.05N and np(1 - p)< 10.C. Approximately normal because ns0.05N and np(1 - p) < 10.D. Not normal because ns0.05N and np(1 - p) 2 10.Determine the mean of the sampling distribution of p.HA =(Round to one decimal place as needed.)Determine the standard deviation of the sampling distribution of p.OA =(Round to six decimal places as needed.)(b) What is the probability of obtaining x= 32 or more individuals with the characteristic? That is, what is P(p20.64)?P(20.64) =(Round to four decimal places as needed.)(c) What is the probability of obtaining x = 27 or fewer individuals with the characteristic? That is, what is P(p<0.54)?P(os0.54) =(Round to four decimal places as needed.)%3D

Given,n=50p=0.6np(1-p)=50×0.6×0.4=12≥10The sampling distribution of p^ is Approximately normal because n≤0.05N andnp(1-p)≥10.μp^=p=0.6σp^=p(1-p)nσp^=0.6×0.450σp^=0.069282Required probability is P(p^≥0.64)=Pp^-μp^σp^≥0.64-μp^σp^=PZ≥0.64-0.60.069282=P(Z≥0.5774)=0.2818P(p^≥0.64)=0.2818Required probability is P(p^≤0.54)=Pp^-μp^σp^≤0.54-μp^σp^=PZ≤0.54-0.60.069282=P(Z≤-0.8660)=0.1932P(p^≤0.54)=0.1932