Salesperson Ratings and Advancement Probability | CFA® Level 1 Exam

Average Sales Ability and Good Potential for Advancement

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Question

Each salesperson in a large department store chain 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 are the 500 salespeople were cross classified into the following table.

Sales Ability Potential for Advancement

Fair Good Excellent -

Below Average 161222 -

Average 456045 -

Above Average 9372135 -

What is the probability that a salesperson selected at random will have average sales ability and good potential for advancement?

Answers

Explanations

Click on the arrows to vote for the correct answer

A. B. C. D. E.

C

Prob. of selecting a person with average sales ability: (45 + 60 + 45)/500 = 3/10. Prob. of selecting good potential amongst those with average sales ability:

60/150. Therefore: 3/10*6/15 = 0.12.

To determine the probability that a salesperson selected at random will have average sales ability and good potential for advancement, we need to find the corresponding cell in the cross-classification table and calculate the probability based on the total number of salespeople.

Looking at the table provided, we can see that the cell for "Average" sales ability and "Good" potential for advancement is 456045.

To calculate the probability, we need to divide the number of salespeople in the cell by the total number of salespeople in the entire table.

To find the total number of salespeople, we sum up the values in all the cells:

Total = 161222 + 456045 + 9372135 = 9994402

Now, we can calculate the probability:

Probability = Number of salespeople in cell / Total number of salespeople

Probability = 456045 / 9994402 ≈ 0.0457

Therefore, the probability that a salesperson selected at random will have average sales ability and good potential for advancement is approximately 0.0457.

However, none of the given answer choices match this result. Therefore, the correct answer is "B. None of these answers."

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