Suppose a simple random sample of size n = 200 is obtained from a population whose size is N = 10,000 and whose population proportion with a specified characteristic is p = 0.8.
(a) Describe the sampling distribution of p.
Choose the phrase that best describes the shape of the sampling distribution below.
A. Not normal because n ≤ 0.05N and np(1 - p) ≥ 10.
B. Approximately normal because n ≤ 0.05N and np(1 - p) ≥ 10.
C. Not normal because n ≤ 0.05N and np(1 - p) < 10.
D. Approximately normal because n ≤ 0.05N and np(1 - p) < 10.
Determine the mean of the sampling distribution of p.
μ_p = (Round to one decimal place as needed.)
Determine the standard deviation of the sampling distribution of p.
σ_p = (Round to six decimal places as needed.)
(b) What is the probability of obtaining x = 168 or more individuals with the characteristic? That is, what is P(p ≥ 0.84)?
P(p ≥ 0.84) = (Round to four decimal places as needed.)
(c) What is the probability of obtaining x = 156 or fewer individuals with the characteristic? That is, what is P(p ≤ 0.78)?
P(p ≤ 0.78) = (Round to four decimal places as needed.)