A sample of 25 observations is taken from 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 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 $\geq$ 5 and n(1-P) $\geq$ 5
D) approximately normal if np > 30 and n(1-P) > 30

Quizplus · Accepted Answer

The sampling distribution of $\bar{p}$ is approximately normal if both np and n(1-p) are greater than or equal to 5, according to the Central Limit Theorem for proportions.

A Sample of 25 Observations Is Taken from an Infinite pˉ\bar { p }pˉ​

A Sample of 25 Observations Is Taken from an Infinite $\bar { p }$