A data set has a mean of 60 and a standard deviation of 5. Which of the following might possibly be true?
A)More than 90% of the data values are between 45 and 75.
B)No less than 30% of the data values are less than 50 or greater than 70.
C)No more than 50% of the data values are between 50 and 70.
D)At least 15% of the data values are less than 45 or greater than 75.

Question

Quizplus · Accepted Answer

According to the empirical rule (or 68-95-99.7 rule), for a normally distributed dataset, approximately 95% of the data falls within two standard deviations of the mean. Here, two standard deviations from the mean (60) would be 50 to 70 (60 ± 2*5), suggesting that more than 90% of the data values being between 45 and 75 is plausible, as it extends beyond the range covered by two standard deviations. Choices B, C, and D contradict the empirical rule's implications for the distribution of data around the mean and standard deviations.

A Data Set Has a Mean of 60 and a Standard