Suppose a simple random sample of size nequals=200200 is obtained from a population whose size is Upper N equals 15 comma 000N=15,000 and whose population proportion with a specified characteristic is p equals 0.2 .p=0.2. (a) Describe the sampling distribution of ModifyingAbove p with caretp. Choose the phrase that best describes the shape of the sampling distribution below. A. Approximately normal because n less than or equals 0.05 Upper Nn0.05N and np left parenthesis 1 minus p right parenthesis greater than or equals 10.np(1p)10.Your answer is correct. B. Not normal because n less than or equals 0.05 Upper Nn0.05N and np left parenthesis 1 minus p right parenthesis less than 10.np(1p)<10. C. Approximately normal because n less than or equals 0.05 Upper Nn0.05N and np left parenthesis 1 minus p right parenthesis less than 10.np(1p)<10. D. Not normal because n less than or equals 0.05 Upper Nn0.05N and np left parenthesis 1 minus p right parenthesis greater than or equals 10.np(1p)10. Determine the mean of the sampling distribution of ModifyingAbove p with caretp. mu Subscript ModifyingAbove p with caret Baseline equalsp=0.20.2 (Round to one decimal place asneeded.) Determine the standard deviation of the sampling distribution of ModifyingAbove p with caretp. sigma Subscript ModifyingAbove p with caretpequals=0.0282840.028284 (Round to six decimal places asneeded.) (b) What is the probability of obtaining x=50 or more individuals with thecharacteristic? Thatis, what is P(ModifyingAbove p with caretpgreater than or equals0.250.25)? P(ModifyingAbove p with caretpgreater than or equals0.250.25)equals=nothing (Round to four decimal places asneeded.)