Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8. The mean and the standard deviation of the sampling distribution of the sample means are
A) 8.7 and 1.94.
B) 36 and 1.94.
C) 36 and 1.86.
D) 36 and 8.

Question

Quizplus · Accepted Answer

The mean of the sampling distribution of the sample means is equal to the population mean, which is 36. 
The standard deviation of the sampling distribution of the sample means is equal to the population standard deviation divided by the square root of the sample size, which is 8/sqrt(17) = 1.86. Therefore, the answer is choice C.

Random Samples of Size 17 Are Taken from a Population