Question

The scores on an exam are normally distributed, with a mean of 85 and a standard deviation of 8. What percent of the scores are greater than 93?

Answer 1

16%

Explanation:

Find the z-score.

z = (x − μ) / σ

z = (93 − 85) / 8

z = 1

This means 93 is one standard deviation above the mean.

According to the empirical rule, 68% of a normal distribution is between -1 and +1 standard deviations. So 32% is either less than -1 or greater than +1 standard deviations. Normal curves are symmetrical, so 16% is greater than +1 standard deviations.