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: Analyze the area

The total area to the left of \(z = 0\) is \(0.5\). The given area is \(0.9545\). So the area to the left of \(z\) is \(0.5-(0.9545 - 0.5)=0.0455\).

Step2: Use the standard normal distribution table

Looking up the value \(0.0455\) in the standard - normal distribution table (the body of the table). The closest value to \(0.0455\) in the standard normal table. The \(z\) - value corresponding to an area of \(0.0455\) is \(z=-1.69\) (since the area is to the left of \(z = 0\) and the \(z\) - score is negative).

Answer:

\(z=-1.69\)