CFA Level 1: Probability of Salesperson with Above Average Sales Ability and Excellent Potential for Advancement

Probability of Salesperson with Above Average Sales Ability and Excellent 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 for 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 above average sales ability and excellent potential for advancement?

Answers

Explanations

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A. B. C. D. E.

E

We need the prob(above average) = (93 + 72 + 135)/500 and prob(excellent given above average) = 135/300. Therefore 300/500*135/300 = 0.27

To determine the probability that a salesperson selected at random will have above average sales ability and excellent potential for advancement, we need to calculate the ratio of the number of salespeople who possess both traits to the total number of salespeople.

From the table given, we can see that the number of salespeople who have above average sales ability and excellent potential for advancement is 7.

To calculate the total number of salespeople, we need to sum up all the values in the table: 161 + 222 + 456 + 45 + 937 + 2,135 + 5 = 3,961

Therefore, the probability is calculated as:

Probability = Number of salespeople with above average sales ability and excellent potential for advancement / Total number of salespeople

Probability = 7 / 3,961

Calculating this ratio, we find that the probability is approximately 0.00177.

Now, we need to find the closest answer choice provided in the options.

A. 0.20 B. 0.50 C. None of these answers D. 0.75 E. 0.27

The closest answer choice to 0.00177 is E. 0.27. However, this is not the correct answer. None of the answer choices provided accurately represents the calculated probability.

Therefore, the correct answer choice is C. None of these answers.

It's important to note that the information provided in the question is incomplete. The table is missing data for the number of salespeople in the "Fair" potential for advancement category. Without that information, we cannot accurately determine the probability.

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