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# relative frequency approach

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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.

#### Solution Preview

Hello!

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.

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## Pioneer Aircraft: Probability of Planes Sold

Pioneer Aircraft Co. sells private, single-engine planes. Most sales are for customers engaged in private and leisure flying. In a 50-week period, sales in the past five years have averaged to the following:

PLANES SOLD WEEKS THIS NUMBER SOLD
0 40
1 8
2 1
3 1

1. Determine the probability of each number of planes sold—of 0, 1, 2, 3—in a 50-week period. (Pioneer sales office is closed the other two weeks of the year.)

2. Decide what approach (objective approach, subjective approach, relative frequency approach) is best used to determine probability. Distinguish between the approaches to make it clear that the approach used was the best fit for these airplane sales.

3. Determine if the approach would change if we also needed to track sales of some planes with GPS installed.

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