Question

In a normally distributed data set with a mean of 24 and a standard deviation of 4.2, what percentage of the data would be between 19.8 and 28.2 and why

Answer 1

By the Empirical Rule, 68% of the data would be between 19.8 and 28.2

Explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 24

Standard deviation = 4.2

What percentage of the data would be between 19.8 and 28.2

19.8 = 24 - 4.2

28.2 = 24 + 4.2

So within one standard deviation of the mean

By the Empirical Rule, 68% of the data would be between 19.8 and 28.2