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 cumulative probability for \(z = 1.28\)

Using the standard normal table or a calculator with a normal - distribution function (e.g., in Excel NORM.S.DIST(1.28,TRUE)), we get \(P(Z\leq1.28)\).
\(P(Z\leq1.28)=0.8997\)

Step2: Find the cumulative probability for \(z=-0.83\)

Using the standard normal table or a calculator with a normal - distribution function (e.g., in Excel NORM.S.DIST(-0.83,TRUE)), we get \(P(Z\leq - 0.83)\).
\(P(Z\leq - 0.83)=0.2033\)

Step3: Calculate the area between \(z=-0.83\) and \(z = 1.28\)

The area \(A\) between two \(z\) - scores \(z_1\) and \(z_2\) (\(z_1Here, \(z_1=-0.83\) and \(z_2 = 1.28\), so \(A=P(Z\leq1.28)-P(Z\leq - 0.83)\)
Substitute the values: \(A=0.8997 - 0.2033\)
\(A = 0.6964\)

Answer:

\(0.6964\)