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 area to the left of \(z = 0\)

The total area under the standard - normal curve is \(1\). The area to the right of \(z = 0\) is \(0.5\).

Step2: Calculate the area to the left of \(z\)

Let \(A\) be the area to the left of \(z\). We know that the area from \(z\) to \(0\) plus the area from \(0\) to \(+\infty\) is \(0.9783\). So the area to the left of \(z\) is \(A=1 - 0.9783=0.0217\).

Step3: Look up the \(z\) - value in the standard - normal table

Looking up the value \(0.0217\) in the standard - normal distribution table (the body of the table). The closest value to \(0.0217\) in the standard - normal table. The \(z\) - value corresponding to an area of \(0.0217\) is \(z=- 2.01\) (since the area is to the left of \(0\), \(z\) is negative).

Answer:

\(-2.01\)