Question

In an all boys school, the heights of the student body are normally distributed with amean of 71 inches and a standard deviation of 4.5 inches. Using the empirical rule,what percentage of the boys are between 62 and 80 inches tall?

Answer 1

Explanation

Since the mean is 71 inches and a standard deviation of 4.5 inches.

Using the empirical rule

Firstly, for one standard deviation

$\begin{gathered} \mu-\sigma=71-4.5=66.5 \\ \mu+\sigma=71+4.5=75.5 \end{gathered}$

68% of people have heights between 66.5 and 75.5.

We will check then check for two standard deviations

$\begin{gathered} \mu-2\sigma=71-9=62 \\ \mu+2\sigma=71+9=80 \\ \end{gathered}$

95% of people will have height between 62 and 80.