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 lookup

We know that for a standard normal distribution $N(0,1)$, if we want to find the area between $z_1=- 0.81$ and $z_2 = 1.24$, we first look up the cumulative - distribution function values in the standard normal table. The cumulative - distribution function $\varPhi(z)$ gives the area to the left of $z$ under the standard normal curve.
$\varPhi(-0.81)$ and $\varPhi(1.24)$ are the values we need to find.
From the standard normal table, $\varPhi(-0.81)=0.2090$ and $\varPhi(1.24) = 0.8925$.

Step2: Calculate the area between the two z - values

The area between $z_1=-0.81$ and $z_2 = 1.24$ is given by $\varPhi(1.24)-\varPhi(-0.81)$.
$A=\varPhi(1.24)-\varPhi(-0.81)=0.8925 - 0.2090=0.6835$

Answer:

$0.6835$