Question

Describe the sampling distribution of ModifyingAbove p with caret. Assume the size of the population is 15 comma 000. nequals200​, pequals0.4 Choose the phrase that best describes the shape of the sampling distribution of ModifyingAbove p with caret below. A. Approximately normal because n less than or equals 0.05 Upper N and np left parenthesis 1 minus p right parenthesis less than 10. B. Not normal because n less than or equals 0.05 Upper N and np left parenthesis 1 minus p right parenthesis less than 10. C. Approximately normal because n less than or equals 0.05 Upper N and np left parenthesis 1 minus p right parenthesis greater than or equals 10. D. Not normal because n less than or equals 0.05 Upper N and np left parenthesis 1 minus p right parenthesis greater than or equals 10. Determine the mean of the sampling distribution of ModifyingAbove p with caret. mu Subscript ModifyingAbove p with caret Baseline equals nothing ​(Round to one decimal place as​ needed.) Determine the standard deviation of the sampling distribution of ModifyingAbove p with caret. sigma Subscript ModifyingAbove p with caret Baseline equals nothing ​(Round to three decimal places as​ needed.)

Answer 1

Describe the sampling distribution of ModifyingAbove p with caret. Assume the size of the population is 15 000. n=200​, p=0.4 Choose the phrase that best describes the shape of the sampling distribution of ModifyingAbove p with caret below.

C. Approximately normal because n less than or equals 0.05 Upper N and np left parenthesis 1 minus p right parenthesis greater than or equals 10.

n=200 <    0.05*N=0.05*15000=750

np=0.4*200=80   and (1-p)*n=0.6*200 =120 both are > 10.

Determine the mean of the sampling distribution of ModifyingAbove p with caret.

mu Subscript ModifyingAbove p with caret Baseline equals 0.4 ​(Round to one decimal place as​ needed.)

Determine the standard deviation of the sampling distribution of ModifyingAbove p with caret. sigma Subscript ModifyingAbove p with caret Baseline equals 0.035 ​(Round to three decimal places as​ needed.)

Standard deviation = sqrt(p*(1-p)/n) = sqrt( 0.4*0.6/200) =0.034641016