The scores of a class are normally distributed with a mean of 82 and a standard deviation of 8. What is the mean of the sampling distribution of the sample mean, , if a sample of 64 students is selected at random from all students taking that course?
A) 64
B) between 74 and 90
C) between 78 and 86
D) 82

Question

The scores of a class are normally distributed with a mean of 82 and a standard deviation of 8. What is the mean of the sampling distribution of the sample mean,  , if a sample of 64 students is selected at random from all students taking that course?
A) 64 
B) between 74 and 90 
C) between 78 and 86 
D) 82

Quizplus · Accepted Answer

The mean of the sampling distribution of the sample mean is equal to the population mean, which is 82. Therefore, the answer is D. Choice A is incorrect because it is simply the size of the sample, not the mean of the sampling distribution. Choices B and C are incorrect because they give a range of values, but we only want the mean of the sampling distribution.

The Scores of a Class Are Normally Distributed with a Mean