Question

When Rashaad goes bowling, his scores are normally distributed with a mean of 175and a standard deviation of 13. Using the empirical rule, determine the interval thatwould represent the middle 68% of the scores of all the games that Rashaad bowls.

Answer 1

Recall the following rule of thumb for emperical rule.

Given a normally distributed data,

68% of the data lies within 1 standard deviation away from the mean.

95% of the data lies within 2 standard deviation away from the mean.

99.7% of the data lies within 3 standard deviation away from the mean.

Given a mean of 175, and a standard deviation of 13

Solve for 68% of the interval

$\begin{gathered} 175\pm13 \\ \\ \text{Upper Limit} \\ 175+13=188 \\ \\ \text{Lower Limit} \\ 175-13=162 \end{gathered}$

Therefore, the middle 68% of the scores of all the games that Rashaad bowls is between 162 and 188.