Chapter 11.5, Problem 13PPS

To determine

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

Answer to Problem 13PPS

The value of z is -1, the position of X=18.7 is 1 Standard deviations less than the mean.

Explanation of Solution

Given information:

  $\begin{array}{l}\mu =19.6\\ X=18.7\\ \sigma =0.9\end{array}$

Formula used:

  $z=\frac{X-\mu }{\sigma }$

  $z=\frac{X-\mu }{\sigma }$

Given,

  $\begin{array}{l}\mu =19.6\\ X=18.7\\ \sigma =0.9\end{array}$

  $\begin{array}{l}z=\frac{X-\mu }{\sigma }\\ z=\frac{18.7-19.6}{0.9}\\ z=\frac{-0.9}{0.9}\\ z=-1\end{array}$

The z-value that corresponds to $X=18.7$ is approximately -1. Therefore, 18.7 is 1 Standard deviations less than the mean.