Use the Empirical Rule to Describe Data That Are Bell Shaped
-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 84 and 3 , respectively, and the distribution of scores is bell shaped. What percentage of test-takers scored better than a trainee who scored 75 ?
A) approximately $99.85 \%$
B) approximately $84 \%$
C) approximately $95 \%$
D) approximately $97.5 \%$

Question

Quizplus · Accepted Answer

Given the distribution is bell-shaped, we can apply the Empirical Rule. A score of 75 is 3 standard deviations below the mean (84 - 3*3 = 75). According to the Empirical Rule, 99.7% of the data falls within 3 standard deviations of the mean, leaving 0.3% outside. Since 75 is below the mean, approximately 99.85% of test-takers scored better than a score of 75 (100% - 0.15%).

Use the Empirical Rule to Describe Data That Are Bell 99.85%99.85 \%99.85%

Use the Empirical Rule to Describe Data That Are Bell $99.85 \%$