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: Use the standard normal distribution table

The standard normal distribution table gives the cumulative probability \(P(Z < z)\). Here, the area to the left of \(z\) is \(0.0047\).

Step2: Look up the value in the table

Looking for the value closest to \(0.0047\) in the body of the standard - normal table. The \(z\) - value corresponding to a cumulative probability of approximately \(0.0047\) is \(z=- 2.58\) (by checking the standard normal distribution table: for \(z = - 2.5\), looking at the row for \(z=-2.5\) and the column for \(0.08\), the cumulative probability \(P(Z < - 2.58)=0.0049\) which is very close to \(0.0047\) and considering the precision of the table).

Answer:

\(-2.58\)