Question

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. the area of the shaded region is (round to four decimal places as needed.)

Explanation:

Step1: Use z - table values

We know that for a standard - normal distribution, we need to find the cumulative distribution function values for the given z - scores. The cumulative distribution function of a standard - normal distribution $\varPhi(z)$ gives the area to the left of the z - score.
Let $z_1=-0.98$ and $z_2 = 1.24$. We want to find $P(-0.98From the standard - normal table, $\varPhi(-0.98)=0.1635$ and $\varPhi(1.24)=0.8925$.

Step2: Calculate the area of the shaded region

The area between two z - scores $z_1$ and $z_2$ is given by $P(z_1So, $P(-0.98 < Z<1.24)=\varPhi(1.24)-\varPhi(-0.98)=0.8925 - 0.1635=0.7290$.

Answer:

$0.7290$