A population has a mean of 100 and a standard deviation of 15. If samples of size N = 25 are randomly drawn from this population, then what proportion of sample means will fall between 97 to 103?
A).6826
B).3413
C).5000
D).9544

Question

Quizplus · Accepted Answer

The distribution of sample means of size 25 will follow a normal distribution. The mean of the sample means will still be 100, but the standard deviation will be 15/sqrt(25) = 3. Therefore, we need to find the probability that a sample mean falls between (97-100)/3 = -1 and (103-100)/3 = 1.

Using a standard normal distribution table, the proportion of values falling between -1 and 1 is 0.6826 or 68.26%. Therefore, the answer is A.

A Population Has a Mean of 100 and a Standard