Question

In Exercises 9–12, find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1.

Short answer

The area of the shaded region is 0.6700.

Step-by-step solution

Given information

The graph for standard normal distribution of bone density scores is given with a shaded region.

State the relationship between area and probability 

The standard normal curve encloses an area of 1 unit under the curve. Thus, the area under the curve would have a one-to-one correspondence with the probability of getting a random value in the range.

The left-tailed areas or cumulative probabilities can be obtained using the standard normal table.

Find the probability

It is required to compute the area to the left of the z-score 0.44.

Using the standard normal table, the area is obtained from the table in the cell with row value 0.4 and the column value 0.04, which is obtained as 0.6700.

Mathematically, it is expressed in the following manner:

$$\begin{gathered} \text{Area}\text{to}\text{the}\text{left}\text{of}0.44=P\left(Z<0.44\right) \\ =0.6700 \end{gathered}$$

Thus, the shaded area to the left of 0.44 is equal to 0.6700.