Question

Bone Density Test.

In Exercises 1–4, assume that scores on a bone mineral density test are normally distributed with a mean of 0 and a standard deviation of 1.

Bone Density Sketch a graph showing the shape of the distribution of bone density test scores.

Short answer

The graph for the shape of distribution of bone density test scores is shown below:

Step-by-step solution

Given information

The bone mineral density test scores are normally distributed with mean value of 0 and standard deviation of 1.

Describe the random variable

Let Z be the random variable for bone mineral density test scores.

$$\begin{gathered} Z~N\left(\mu ,{\sigma }^2\right) \\ ~N\left(0,1^2\right) \end{gathered}$$

The shape of the curve is expected to be bell-shaped, symmetric at mean value of 0.

Sketch the graph

The steps to sketch the graph are:

1. Draw horizontal axis with values extending from –3 to 3 with a gap of 1 unit each.
2. Sketch a bell shape curve such that it increases from –3 to 0 and then decreases smoothly from 0 to 3, maintaining symmetry at 0.

The graph is shown below: