Question

find the $z$ value that corresponds to the given area in the figure below. use the standard normal distribution table and enter the answer to 2 decimal places. (note: figure not drawn to scale.)

Explanation:

Step1: Find the cumulative area

The total area under the standard - normal curve is \(1\). The area to the left of \(z\) is \(1 - 0.2236=0.7764\).

Step2: Look up the \(z\) - value in the standard - normal table

We look for the value \(0.7764\) in the body of the standard - normal distribution table (the \(z\) - table).
In the \(z\) - table, the value closest to \(0.7764\) is \(0.7764\) itself.
The row corresponding to \(0.7\) and the column corresponding to \(0.06\) gives a \(z\) - value of \(z = 0.76\).

Answer:

\(z = 0.76\)