A data set has a mean of 50 and a standard deviation of 10. Using the empirical rule, what percentage of data falls between 30 and 70?

Question

Accepted Answer

Approximately 95%. The range from 30 to 70 extends 2 standard deviations below and above the mean: 50 - 2(10) = 30 and 50 + 2(10) = 70. According to the empirical rule, approximately 95% of data in a normal distribution falls within 2 standard deviations of the mean.

Approximately 68% is the percentage within 1 standard deviation (40 to 60 in this case), not 2 standard deviations. Approximately 99.7% is the percentage within 3 standard deviations (20 to 80 in this case). Approximately 50% represents the data on one side of the mean, which is not related to the standard deviation intervals.

Applying the empirical rule to specific data sets is an important skill on the DSST exam. Students must be able to calculate the boundaries for 1, 2, and 3 standard deviations from the mean and apply the 68-95-99.7 percentages. This skill is essential for understanding the spread and distribution of data in context.

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