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: Find the area to the left of \(z = 1.28\)

Using the standard normal distribution table or a calculator, the area to the left of \(z=1.28\) is \(P(Z < 1.28)=0.8997\)

Step2: Find the area to the left of \(z=- 0.97\)

Using the standard normal distribution table or a calculator, the area to the left of \(z = - 0.97\) is \(P(Z < - 0.97)=0.1660\)

Step3: Calculate the area of the shaded region

The area of the shaded region is \(P(-0.97<Z<1.28)=P(Z < 1.28)-P(Z < - 0.97)\)
Substitute the values: \(0.8997 - 0.1660=0.7337\)

Answer:

\(0.7337\)