Chapter 3.1, Problem 3.4E

(a)

To determine

To explain whether the z score = -1.45 or z = 0.50, out of these which one shows more healthier person.

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) whereas the z score equal to 0.50 that the bone density of the person is 0.5 standard deviation above then the mean.

The higher the bone density means that healthier the person, therefore the person which have the z score equal to 0.50 is more healthier.

(b)

To determine

To calculate the value of standard deviation for the bone density of 35 year old.

Answer to Problem 3.4E

Standard deviation = 8

Explanation of Solution

Given:

  $\begin{array}{l}z=0.50\\ \mu =944\\ x=948\end{array}$

Formula used:

  $z=\frac{x-\mu }{\sigma }$

Calculation:

  $\begin{array}{l}z=\frac{x-\mu }{\sigma }\\ 0.50=\frac{948-944}{\sigma }\\ \sigma =\frac{948-944}{0.50}\\ \sigma =8\end{array}$