Assume that a set of test scores in an Introduction to Finance class is normally distributed with a mean of 72 and a standard deviation of 8.Use the 68-95-99.7 rule to find the percentage of scores less than 56.
A)0.15%
B)0.3%
C)2.5%
D)5%
E)95%

Question

Quizplus · Accepted Answer

According to the 68-95-99.7 rule (or the empirical rule), approximately 68% of the data within a normal distribution falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations. A score of 56 is two standard deviations below the mean (72 - 2*8 = 56). Therefore, 2.5% of the scores are less than 56, as the lower tail (below -2 standard deviations) accounts for half of the remaining 5% (100% - 95% = 5%) not within two standard deviations of the mean.

Assume That a Set of Test Scores in an Introduction