Question

Suppose that the average number hours a student works out per week is 2.63 with a sample standard deviation of 2.52. Would it be unusual for a student to work out 8 hours a week? What about 0 times a week? Justify your answer using statistical reasoning.

Answer 1

A value can be considered unusual if it is more than 2 standard deviations from mean (Z score > 2 or Z score < -2)

Z = (X - mean)/standard deviation

Z score corresponding to 8 is (8 - 2.63)/2.52 = 2.13

Therefore, it will be unusual for a student to work out 8 hours a week.

Z score corresponding to 0 = (0 - 2.63)/2.52 = -1.04

It is not unusual for a student to work out 0 times a week.