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Question

# The quantitative data set under consideration has roughly a bell-shaped distribution. Apply the empirical rule to solve each exercise. The data set has mean 15 and standard deviation 2. Approximately what percentage of the observations lie between 13 and 17?

Solution

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Step 1
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Given:

$\overline{x}=15$

$s=2$

DEFINITIONS

$\textbf{Empirical rule}$ (for roughly bell-shaped distributions)

Approximately 68% of the observations are within 1 standard deviation of the mean.

Approximately 95% of the observations are within 2 standard deviations of the mean.

Approximately 99.7% of the observations are within 3 standard deviations of the mean.

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