Suppose a simple random sample of size n= 75 is obtained from a population whose size is N= 30,000 and whose population proportion with a specified characteristic is p = 0.4. Complete parts
K
(a) through (c) below.
3
(a) Describe the sampling distribution of p.
Choose the phrase that best describes the shape of the sampling distribution below.
く
A. Approximately normal because n≤ 0.05N and np(1 - p) < 10.
B.
Not 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.
H, = (Round to one decimal place as needed.)
Determine the standard deviation of the sampling distribution of p. op =__ (Round to six decimal places as needed.)
(b) What is the probability of obtaining x= 33 or more individuals with the characteristic? That is, what is P(ô≥0.44)?
P(ô≥ 0.44) = 24.5 (Round to four decimal places as needed.)
(c) What is the probability of obtaining x = 24 or fewer individuals with the characteristic? That is, what is P(ô ≤0.32)?
P(Ô≤0.32) = 244.5 (Round to four decimal places as needed.)