Chapter 3.1, Problem 3.3E

(a)

To determine

To explain the meaning of z score equal to -1.45 in regards of bone density of 25 year old women.

Explanation of Solution

The z score tells us how far the particular value is from the mean in terms of standard deviation. Negative sign means that the value is less than mean and positive sign means that value is more than mean.

Here, the z score equal to -1.45 means that the her bone density is 1.45 standard deviations less than the mean (956).

(b)

To determine

To calculate the value of standard deviation.

Explanation of Solution

Given:

  $\begin{array}{l}z=-1.45\\ \mu =956\\ x=948\end{array}$

Formula used:

  $z=\frac{x-\mu }{\sigma }$

Calculation:

  $\begin{array}{l}z=\frac{x-\mu }{\sigma }\\ -1.45=\frac{948-956}{\sigma }\\ \sigma =\frac{948-956}{-1.45}\\ \sigma =5.52\end{array}$