# Probability Question

Each salesperson at stiles compton is rated either below average, average, or above average with respect to sales ability. Each salesperson is also rated with respect to his or her potential for advancement: either fair, good or excellent. These traits for the 500 sales people were cross classified into the following table.

fair good excellent

below average 16 12 22

average 45 60 45

above average 93 72 135

a. What is this table called?

b. What is the probability a salesperson selected at random will have above average sales ability and excellent potential for advancement?

c. Construct a tree diagram showing all probabilities, conditional probability, and joint probability.

#### Solution Preview

a. What is this table called?

This is a contingency table. It shows the observed frequencies of data classified according to two variables. Here, the two variables are sales ability and potential for advancement.

b. What is the probability a salesperson selected at random will have above average sales ability and excellent potential for advancement?

There are 500 total sales people. The probability that they will have above average sales ability is 300/500 = 0.60. ...

#### Solution Summary

The solution includes answers and explanations to parts a, b, and c of the question, and includes a tree diagram for the different probabilities.