The dean of admissions in a large university has determined that the scores of the freshman class in a mathematics test are normally distributed with a mean of 82 and a standard deviation of 8. Based on this information, what is the mean of the sampling distribution of the sample mean if a sample of 64 students is selected at random from the entire freshman class?
A) between 74 and 90
B) between 78 and 86
C) 64
D) 70
E) 82

Question

The dean of admissions in a large university has determined that the scores of the freshman class in a mathematics test are normally distributed with a mean of 82 and a standard deviation of 8. Based on this information, what is the mean of the sampling distribution of the sample mean  if a sample of 64 students is selected at random from the entire freshman class?
A) between 74 and 90 
B) between 78 and 86 
C) 64 
D) 70 
E) 82

Quizplus · Accepted Answer

According to the central limit theorem, the sampling distribution of the sample mean is also normally distributed with a mean equal to the population mean, which is 82 in this case, and a standard deviation of σ/√n, where σ is the population standard deviation and n is the sample size. Therefore, the standard deviation of the sampling distribution is 8/√64 = 1. Since the mean of the sampling distribution is the same as the population mean, the answer is E) 82.

The Dean of Admissions in a Large University Has Determined