Chapter 11.5, Problem 4CYU

To determine

To find: The missing variable and the position of X.

Answer to Problem 4CYU

The value of z is 0.69, the position of X=18 is 0.69 Standard deviations more than the mean.

Explanation of Solution

Given information:

  $\begin{array}{l}\mu =89\\ X=81\\ \sigma =11.5\end{array}$

Formula used:

  $z=\frac{X-\mu }{\sigma }$

  $z=\frac{X-\mu }{\sigma }$

Given,

  $\begin{array}{l}\mu =89\\ X=81\\ \sigma =11.5\end{array}$

  $\begin{array}{l}z=\frac{X-\mu }{\sigma }\\ z=\frac{81-89}{11.5}\\ z=\frac{-8}{11.5}\\ z=\boxed{-0.69}\end{array}$

The z-value that corresponds to $X=81$ is approximately -0.69. Therefore, 18 is 0.69 Standard deviations less than the mean.