# relative frequency approach

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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#### Solution Preview

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a. The relative frequency approach requires you to divide the absolut efrequency for each event (for example, the event that 1 test was taken had an absolute frequency of 10) by the total number of observations. In this case, the total number of observations (students) is 20. Therefore, the probability ...

#### Solution Summary

The relative frequency approach is applied.