A data set has a mean of 70 and a standard deviation of 10. Which of the following might possibly be true?
A) At least 15% of the data values are less than 40 or greater than 100.
B) More than 90% of the data values are between 40 and 100.
C) No more than 50% of the data values are between 50 and 90.
D) No less than 30% of the data values are less than 50 or greater than 90.

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 (70) would be 50 (70-20) and 90 (70+20), meaning more than 90% of the data values are expected to be between 40 and 100, making option B a possibility.

A Data Set Has a Mean of 70 and a Standard