Question

The scores on an exam are normally distributed with a mean of 74 and a standard deviation of 7. What percent of the scores are greater than 81?

A. 50%

B. 13.5%

C. 84%

D. 16%

Answer 1

The difference between 81 and the mean is
81 - 74 = 7
This is exactly the value of the standard deviation. You know that the "empirical rule" tells you 68% of all scores lie within 1 standard deviation of the mean. That tells you 32% of all scores lie beyond 1 standard deviation from the mean.

The normal distribution is symmetrical, so half of those (16%) lie above 1 standard deviation above the mean; the other half (16%) lie below 1 standard deviation below the mean. We're only concerned with the first group—those scores above 1 standard deviation above the mean.

The appropriate choice is
D. 16%