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

Question

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

Quizplus · Accepted Answer

The sampling distribution of a proportion will be approximately normal with a mean of p and a standard deviation of sqrt((p(1-p))/n). In this case, the mean is 0.20 and the standard deviation is sqrt((0.20(1-0.20))/1000) = 0.01414. Since the sample size is large enough (n>=30), the sampling distribution can be assumed to be approximately normal.

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