Describe the sampling distribution of ModifyingAbove p with caret . Assume the s

Question

Describe the sampling distribution of ModifyingAbove p with caret . Assume the size of the population is 10 comma 000 . nequals 200, pequals 0.1 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 greater than or equals 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. Not normal because n less than or equals 0.05 Upper N and np left parenthesis 1 minus p right parenthesis less than 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.)

Explanation / Answer

a)

N= 10000,n =200, p = 0.1, q = 0.9

Samping can be approximated by normal if

np >= 200*0.1>= 10

nq >=200*0.9 = 9000>=10

n<=0.05N <= 0.05*10000<=500

B. Approximately normal because n_<0.05N and np(1-p)_>10.

b)

Mean of the sampling dist = p = 0.1

sd = (pq/n)^0.5 = [(0.1*0.9)/200]^0.5 = 0.021

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