Question

Suppose a simple random sample of siren. 200 is obtained from a population whose size o N 30,000 and whose population proportion with a specified chap 6 Complete parts though how A. Approximately normal because n <0.05N and nipit - p) 10. OB. Not normal becausen 0.06 and p1-p) < 10 OC. Not normal because nooN and p(1-P) 10. O D. Approximately normal because no.05N and pt-p}<10 P Determine the mean of the sampling distribution of - (Round to one dickemal place as needed) Determine the standard deviation of the sampling dition of 0.0034641 (Round to six decimal places as needed) (b) What is the probability of obtaining x 130 or more individuals with the characteristi? That is what is PP 0657 PP2065) - (Round to four decimal places as needed)

Answer 1

Sampling distribution of p̂ is approximately normal if np >=10 and n (1-p) >= 10
n * p = 200 * 0.6 = 120
n * (1 - p ) = 200 * (1 - 0.6) = 80

Mean = $\mu_{\hat{p}}$ = p = 0.6

Standard deviation = = 0.034641

p(1 - p)/n

X ~ N ( µ = 0.6 , σ = 0.034641 )
P ( X ≥ 0.65 ) = 1 - P ( X < 0.65 )
Standardizing the value
Z = ( X - µ ) / σ
Z = ( 0.65 - 0.6 ) / 0.034641
Z = 1.4434
P ( ( X - µ ) / σ ) > ( 0.65 - 0.6 ) / 0.034641 )
P ( Z > 1.4434 )
P ( X ≥ 0.65 ) = 1 - P ( Z < 1.4434 )
P ( X ≥ 0.65 ) = 1 - 0.9255
P ( X ≥ 0.65 ) = 0.0745