A calculus instructor uses computer aided instruction and allows students to take

A calculus instructor uses computer aided instruction and allows students to take  the midterm exam as many times as needed until a passing grade is obtained. Following is a record of the number of students in a class of 40 who took the test each number of times.

a. Find the expected value of the number of tests taken.
b. Compute the variance and the standard deviation of the number of tests taken.