A normally distributed population with 200 elements has a mean of 60 and a standard deviation of 10. The probability that the mean of a sample of 25 elements taken from this population will be smaller than 56 is:
A) 0.0166 .
B) 0.0228 .
C) 0.3708 .
D) 0.0394 .

Question

A normally distributed population with 200 elements has a mean of 60 and a standard deviation of 10. The probability that the mean of a sample of 25 elements taken from this population will be smaller than 56 is: 
A)  0.0166 . 
B) 0.0228 . 
C) 0.3708 . 
D) 0.0394 .

Quizplus · Accepted Answer

The probability that the mean of a sample of 25 elements taken from this population will be smaller than 56 is 0.0166. This is because the mean of the sample will be normally distributed with a mean of 60 and a standard deviation of 10/sqrt(25) = 2. The probability that the mean of the sample will be smaller than 56 is the area under the normal distribution curve to the left of 56, which is 0.0166.

A Normally Distributed Population with 200 Elements Has a Mean