Question

Given a normally distributed data set with the mean = 108 and the standard deviation = 15, according to the empirical rule, what percent of the data points are between 93 and 123?

Answer 1

Using the empirical rule for a normally distributed dataset with a mean of 108 and a standard deviation of 15, about 95% of the data points are between 93 and 123, which are two standard deviations away from the mean.

Step-by-step explanation:

According to the empirical rule (also known as the 68-95-99.7 rule), for a normally distributed data set, approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. Since you are asking for the percentage between 93 and 123, we are looking at the data within two standard deviations from the mean, as one standard deviation is 15.

Mean = 108, Standard Deviation = 15

• One standard deviation from the mean: 108 ± 15 = [93, 123]
• Two standard deviations from the mean: 108 ± 2(15) = [78, 138]

Therefore, according to the empirical rule, about 95% of the data points lie between the values of 93 and 123, which is two standard deviations from the mean.