Question

find the area under the shaded region. the graph depicts the standard normal distribution with mean 0 and standard deviation 1.
1
0.2776
0.7224
0.5

Explanation:

Step1: Use the property of standard normal distribution

The total area under the standard normal curve is \(1\). The area to the left of \(z = 0\) is \(0.5\).

Step2: Find the area to the left of \(z=-0.59\)

Using the standard - normal table (or z - table), for \(z=-0.59\), the area \(A_{1}=\Phi(-0.59)\). From the z - table, \(\Phi(-0.59)=0.2776\)

Step3: Calculate the area of the shaded region

The area of the shaded region \(A\) is given by \(A = 1-\Phi(-0.59)\) (since the area of the non - shaded part to the left of \(z =-0.59\) is \(\Phi(-0.59)\)). Substitute \(\Phi(-0.59) = 0.2776\) into the formula: \(A=1 - 0.2776=0.7224\)

Answer:

0.7224