Question

Suppose the probability of obtaining a score between 0 and 100 on an test increases monotonically between 0 and 1.00. Is the average score on the
test (a) greater than 50, (b) equal to 50, (c) less than 50 ?

Answer 1

option A is correct

Greater than 50

As the probability of obtaining higher marks increases monotonically the chances that the student will score more than 50 increases.

This can be seen by thinking of a student whose probability of obtaining marks 80 out of 100 is 0.2 and obtaining 20 out of 100 is 0.05 then it is almost sure that he will get marks above 50 because of higher probability assigned to marks above 50.

Thank you !!