Question

Many firms use on-the-job training to teach their employees new software. Suppose you work in the personnel department of a firm that just finished training a group of its employees in new software, and you have been requested to review the performance of one of the trainees on the final test that was given to all trainees. The mean and standard deviation of the test scores are 71 and 3, respectively, and the distribution of scores is bell shaped. What percentage of test-takers scored better than a trainee who scored 62?

a. approximately 97.5%
b. approximately 99.85%
c. approximately 84%
d. approximately 95%

Answer 1

Approximately 99.85% of test-takers scored better than a trainee with a score of 62, according to the Empirical Rule for a bell-shaped distribution.

Step-by-step explanation:

The question asks what percentage of test-takers scored better than a trainee who scored 62 on a test with a mean of 71 and a standard deviation of 3, assuming a bell-shaped distribution of scores. To solve this, we can use the Empirical Rule, as the distribution is bell-shaped.

According to the Empirical Rule, roughly 68% of data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. In this case, a score of 62 is three standard deviations below the mean (since 3 standard deviations are 9 points and 71 - 9 = 62). This means that approximately 99.85% of test-takers scored higher than the score of 62, because the trainee's score falls just outside of three standard deviations from the mean, where over 99% of the data lies.

The correct answer is (b) approximately 99.85%.