Chapter 11.5, Problem 9PPS

To determine

To find: The range of values that represent the outside $5\%$ distribution.

Answer to Problem 9PPS

The range of values that represent the outside $5\%$ distribution is $X<15.9$ , and $X>42.7$ .

Explanation of Solution

Given:

The mean is $29.3$ .

The standard deviation is $6.7$ .

Calculation:

The two tails covers the outside $5\%$ of the distribution. The upper tail has $2.5\%$ of data which is greater than $\mu +2\sigma$ . The lower tail has $2.5\%$ of data which is less than $\mu -2\sigma$ .

Find the upper tail.

  $\begin{array}{c}\mu +2\sigma =29.3+2\left(6.7\right)\\ =42.7\end{array}$

Find the upper tail.

  $\begin{array}{c}\mu -2\sigma =29.3-2\left(6.7\right)\\ =15.9\end{array}$

Therefore, the range of values that represent the outside $5\%$ distribution is $X<15.9$ , and $X>42.7$ .