Question

find the area of the shaded region. the graph depicts the standard normal distribution with mean 0 and standard deviation 1. click to view page 1 of the table. click to view page 2 of the table. the area of the shaded region is (round to four decimal places as needed.)

Explanation:

Step1: Use the standard normal distribution table

The standard normal distribution table (z - table) gives the cumulative probability \(P(Z\leq z)\). For \(z = 0.71\), we look up the value in the z - table.
In the z - table, we first find the row corresponding to \(z=0.7\) and the column corresponding to \(0.01\).
The value in the z - table for \(z = 0.71\) is \(P(Z\leq0.71)=0.7611\).
Since the total area under the standard normal curve is \(1\), and we want the area to the right of \(z = 0.71\) (the shaded region in the right - tailed case shown in the graph), we use the formula \(A=1 - P(Z\leq z)\).

Step2: Calculate the area of the shaded region

Substitute \(z = 0.71\) into the formula \(A = 1 - P(Z\leq z)\).
We know that \(P(Z\leq0.71)=0.7611\), so \(A=1 - 0.7611\).
\(A=0.2389\)

Answer:

\(0.2389\)