A sample of 25 observations is taken from a process (an infinite population). The sampling distribution of $\bar { p }$ is _____. A) not normal since n 30 and n(1 - p) 30

Question

A sample of 25 observations is taken from a process (an infinite population). The sampling distribution of $\bar { p }$ is _____.
A) not normal since n < 30
B) approximately normal because $\bar { p }$ is always normally distributed
C) approximately normal if np ? 5 and n(1 - p) ? 5
D) approximately normal if np > 30 and n(1 - p) > 30

Quizplus · Accepted Answer

The sampling distribution of $\bar{p}$ (the sample proportion) is approximately normal if the sample size n is such that both np and n(1-p) are greater than or equal to 5, according to the rule of thumb for the normal approximation to the binomial distribution.

A Sample of 25 Observations Is Taken from a Process pˉ\bar { p }pˉ​

A Sample of 25 Observations Is Taken from a Process $\bar { p }$