Question: 1.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

1.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 20 who took the test each number of times.

Students Number of Tests

10 1

7 2

2 3

1 4

a.Use the relative frequency approach to construct a probability distribution and show that it satisfies the required condition.

b.Find the expected value of the number of tests taken.

c.Compute the variance.

d.Compute the standard deviation.

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