Question

Describe the sampling distribution of ModifyingAbove p with caret. Assume the size of the population is 25 comma 000. nequals400​, pequals0.2 Choose the phrase that best describes the shape of the sampling distribution of ModifyingAbove p with caret below. A. Not 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 greater than or equals 10. C. Approximately normal because n less than or equals 0.05 Upper N and np left parenthesis 1 minus p right parenthesis less than 10. D. 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. 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

Given that

n = 400 and p = 0.20

population = 25000

first condition,

second condition

np = 400*0.2 = 80 greater than or equal to 10 (satisfied)

and n(1-p) = 400*0.8 = 320 greater than or equal to 10 (satisfied)

option D. 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

mean = p = 0.2

and

standard deviation =