A sample of 92 observations is taken from a process (an infinite population). The sampling distribution of is approximately normal because
A) is always approximately normally distributed
B)the sample size is small in comparison to the population size
C)of the central limit theorem
D)None of the alternative answers is correct.

Question

A sample of 92 observations is taken from a process (an infinite population). The sampling distribution of  is approximately normal because
A) is always approximately normally distributed 
B)the sample size is small in comparison to the population size 
C)of the central limit theorem 
D)None of the alternative answers is correct.

Quizplus · Accepted Answer

According to the central limit theorem, the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the population distribution. In this case, since the sample size is relatively large (92 observations), we can assume that the sampling distribution of the mean is approximately normal. Therefore, choice C is correct. Choice A is not correct because it is not always true that a population or a sample will be normally distributed. Choices B and D are incorrect because they do not explain why the sampling distribution of the mean is approximately normal.

A Sample of 92 Observations Is Taken from a Process