A data set has a mean of 50 and a standard deviation of 10. Which of the following might possibly be true?
A) More than 90% of the data values are between 20 and 80.
B) No more than 50% of the data values are between 30 and 70.
C) No less than 30% of the data values are less than 30 or greater than 70.
D) At least 15% of the data values are less than 20 or greater than 80.

Question

Quizplus · Accepted Answer

According to the empirical rule, for a normal distribution, approximately 68% of the data values fall within one standard deviation of the mean, approximately 95% fall within two standard deviations, and approximately 99.7% fall within three standard deviations.

Option A states that more than 90% of the data values are between 20 and 80. Since 20 and 80 are two standard deviations away from the mean (50), this statement is consistent with the empirical rule. Therefore, option A is possible.

Option B states that no more than 50% of the data values are between 30 and 70. However, since 30 and 70 are within one standard deviation away from the mean, this statement contradicts the empirical rule. Therefore, option B is not possible.

Option C states that no less than 30% of the data values are less than 30 or greater than 70. Since 30 and 70 are within one standard deviation of the mean, this statement is inconsistent with the empirical rule. Therefore, option C is not possible.

Option D states that at least 15% of the data values are less than 20 or greater than 80. Since 20 and 80 are more than two standard deviations away from the mean, only a small percentage of the data values would fall outside this range, making it unlikely that at least 15% would fall outside. Therefore, option D is not possible.

A Data Set Has a Mean of 50 and a Standard