Suppose a simple random sample of size nequals=200200 is obtained from a population whose size is upper n equals 30 comma 000n=30,000 and whose population proportion with a specified characteristic is p equals 0.4 .p=0.4. (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 nn≤0.05n and np left parenthesis 1 minus p right parenthesis greater than or equals 10.np(1−p)≥10. b. not normal because n less than or equals 0.05 upper nn≤0.05n and np left parenthesis 1 minus p right parenthesis greater than or equals 10.np(1−p)≥10. c. not normal because n less than or equals 0.05 upper nn≤0.05n and np left parenthesis 1 minus p right parenthesis less than 10.np(1−p)< 10. d. approximately normal because n less than or equals 0.05 upper nn≤0.05n and np left parenthesis 1 minus p right parenthesis less than 10.np(1−p)< 10. determine the mean of the sampling distribution of modifyingabove p with caretp. mu subscript modifyingabove p with caret baseline equalsμp=0.60.6 (round to one decimal place as needed.) determine the standard deviation of the sampling distribution of modifyingabove p with caretp. sigma subscript modifyingabove p with caretσpequals=0.0350.035 (round to six decimal places as needed.) (b) what is the probability of obtaining xequals=9090 or more individuals with thecharacteristic? that is, what is p(modifyingabove p with caretpgreater than or equals≥0.450.45)? p(modifyingabove p with caretpgreater than or equals≥0.450.45)equals=nothing (round to four decimal places as needed.) (c) what is the probability of obtaining xequals=7474 or fewer individuals with thecharacteristic? that is, what is p(modifyingabove p with caretpless than or equals≤0.370.37)? p(modifyingabove p with caretpless than or equals≤0.370.37)equals=nothing (round to four decimal places as needed.) click to select your answer(s).