A random sample of size 1,000 is taken from a population where p = .20.Describe the sampling distribution of $\hat { p }$.
A)Cannot be determined
B)Approximately normal
C)Skewed to the left
D)Skewed to the right

Question

Quizplus · Accepted Answer

According to the central limit theorem, when the sample size is large enough (n > 30) and the population is not extremely skewed, the sampling distribution of the sample proportion will be approximately normal. In this case, n = 1,000 which is sufficiently large and p = 0.20 is not extremely skewed. Therefore, the sampling distribution of the sample proportion will be approximately normal.

A Random Sample of Size 1,000 Is Taken from a Population