Question

find the = 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 cumulative area to the left of \(z\) is \(1 - 0.2236=0.7764\).

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

In the standard - normal distribution table (the \(z\) - table), we look for the value closest to \(0.7764\).
Looking at the \(z\) - table:
The \(z\) - value corresponding to an area of \(0.7764\) is \(z = 0.76\) (by finding the row and column in the \(z\) - table. For example, if we look at the row for \(0.7\) and the column for \(0.06\), the value in the table is \(0.7764\)).

Answer:

\(0.76\)