A sample of 25 observations is taken from an infinite population. The sampling distribution of 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  is
A) not normal since n < 30. 
B) approximately normal because 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 the proportion follows an approximately normal distribution if np>= 5 and n(1-P)>= 5, which is satisfied by choice C. Choice A is incorrect because the sample size is not the only factor that determines the normality of a sampling distribution. Choice B is incorrect as the normality of the population distribution does not guarantee the normality of the sampling distribution. Choice D is incorrect as it refers to the normality of the sampling distribution of the mean, not the proportion.

A Sample of 25 Observations Is Taken from an Infinite