Many firms use on-the-job training to teach their employees computer programming. Suppose you work in the personnel department of a firm that just finished training a group of its employees
To program, 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 80
And 5, respectively. Assuming nothing is known about the distribution, what percentage of
Test-takers scored above 95?
A)approximately 0.15%
B)at least 89%
C)at most 11%
D)approximately 99.85%

Question

Quizplus · Accepted Answer

Without knowing the exact distribution of the test scores, we can apply the empirical rule if we assume a normal distribution. However, even without assuming this, we know that a score of 95 is 3 standard deviations above the mean (since the mean is 80 and the standard deviation is 5). In a normal distribution, about 99.7% of values lie within 3 standard deviations of the mean, leaving about 0.3% outside. Since 95 is above the mean, approximately half of this 0.3% (or 0.15%) would score above 95, making it a very small percentage. Therefore, the correct answer is that at most 11% of test-takers scored above 95, as this option does not contradict the likely distribution and acknowledges that very few would achieve such a high score.

Many Firms Use On-The-Job Training to Teach Their Employees Computer