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 to the left of \(z = 0\) is \(0.5\). The given area between \(z\) and \(0\) is \(0.4522\). So the cumulative area to the left of \(z\) is \(0.5-0.4522=0.0478\).

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

We look for the value closest to \(0.0478\) in the body of the standard - normal distribution table. The value \(0.0478\) corresponds to a \(z\) - value. Looking at the table, \(z=-1.66\) (since the area is to the left of \(0\), the \(z\) - value is negative).

Answer:

\(-1.66\)