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 property

The area under the standard - normal curve between two z - scores \(z_1\) and \(z_2\) is given by \(P(z_1<Z<z_2)=\Phi(z_2)-\Phi(z_1)\), where \(\Phi(z)\) is the cumulative distribution function of the standard - normal distribution. Here, \(z_1=-0.96\) and \(z_2 = 1.24\).

Step2: Look up values in z - table

From the standard - normal table, \(\Phi(-0.96)=0.1685\) and \(\Phi(1.24)=0.8925\).

Step3: Calculate the area

\(P(-0.96 < Z < 1.24)=\Phi(1.24)-\Phi(-0.96)=0.8925 - 0.1685\).
\(P(-0.96 < Z < 1.24)=0.7240\)

Answer:

\(0.7240\)