Chapter 2.1, Problem 13E

(a)

To determine

To explain: aboutthe standardized score regarding J’s bone density.

Answer to Problem 13E

J’s bone density in hip is 1.45 standard deviation less than the average bone density

Explanation of Solution

Given:

Mean bone density of M = ${\text{948 g/cm}}^{\text{2}}$

Mean bone density of G = ${\text{944 g/cm}}^{\text{2}}$

Since Judy's standardized score is negative this means her bone density in hip is 1.45 standard deviation less than the average bone density in hip of population of 25-year-old women like Judy.

(b)

To determine

To find: the standard deviation of bone density

Answer to Problem 13E

The standard deviation of bone density is $\sigma =5.5172$ .

Explanation of Solution

Calculation:

Judy's results indicate a bone density in hip of $948g/{\text{cm}}^2$ and a standardized score of

  $z=-\mathrm{1.45.}$ In the reference population of 25-year-old women like Judy, the bone density in the hip is $948g/{\text{cm}}^2$ . The standard deviation is calculated below:

  $\begin{array}{l}z(\text{Judy)=}\frac{x-\mu }{\sigma }\\ \Rightarrow -1.45=\frac{948-956}{\sigma }\\ \Rightarrow \sigma =5.5172\end{array}$

Conclusion:

Therefore, the standard deviation of bone density is $\sigma =5.5172$ .