91Ó°ÊÓ

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

The distribution of bone density test score follows the standard normal distribution, and the variable for the bone density test score is denoted by Z.

Thus,

$$\begin{gathered} Z~N\left(\mathrm{μ},{\mathrm{σ}}^2\right) \\ ~N\left(0,1^2\right) \end{gathered}$$

Steps to draw a normal curve:

1. Make a horizontal axis and a vertical axis.
2. Mark the points -3.5, -3.0, -2.5 up to 3.0 on the horizontal axis and points 0, 0.05, 0.10 up to 0.50 on the vertical axis.
3. Provide titles to the horizontal and vertical axes as z and P(z), respectively.
4. Shade the region less than 0.

The shaded area of the graph indicates the probability that the z-score is less than 0.

Referring to the standard normal table for the negative z-score, the cumulative probability of 0 is obtained from the cell intersection for row 0.0 and the column value of 0.00, which is 0.5000.

As the probability and area have a one-to-one correspondence, the probability that the bone density test score is less than 0 is computed as

$P\left(Z<0\right)=0.5000$

Thus, the probability of the bone density test score being less than 0 is 0.5000.