Suppose a simple random sample of size n = 50 is obtained from a population whose size is N = 20,000 and whose population proportion with a specified characteristic is p = 0.6 . Complete parts (a) through (c) below.
(a) Describe the sampling distribution of p.
Choose the phrase that best describes the shape of the sampling distribution below.
Not normal because n LE 0.05N and np(1 -p) GE 10.
Approximately normal because n LE 0.05N and np(1 -p) GE 10.
Approximately normal because n LE 0.05N and np(1 - p) < 10.
Not normal because n LE 0.05N and np(1 -p) < 10.
Determine the mean of the sampling distribution of p.
mu p =
Determine the standard deviation of the sampling distribution of p.
sigma p =
(b) What is the probability of obtaining x = 33 or more individuals with the characteristic? That is what is P(p GE 0.66)?
P(p GE 0.66) =
(c) What is the probability of obtaining x = 29 or fewer individuals with the characteristic? That is, what is P(p LE 0.58)?
P(p LE 0.58) =