Question

Given a normally distributed data set with the mean = 38 and the standard deviation = 3, according to the empirical rule, what percent of the data points are below 41?

a) 68%
b) 84%
c) 95%
d) 99.7%

Answer 1

Approximately 68% of the data points are below 41.

Step-by-step explanation:

To determine the percentage of data points below 41 in a normally distributed data set with a mean of 38 and a standard deviation of 3, we can use the empirical rule. According to the rule, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and more than 99% falls within three standard deviations. Since 41 is one standard deviation above the mean, we can infer that the percentage of data points below 41 is approximately:68%.