Question

find the value of $z_{\alpha}$
$z_{0.33}$
$z_{0.33}=\square$ (round to two decimal places as needed.)

Explanation:

Step1: Understand the meaning of \(z_{\alpha}\)

\(z_{\alpha}\) is the z - score such that the area to the right of \(z_{\alpha}\) under the standard normal curve is \(\alpha\). For \(z_{0.33}\), the area to the right of \(z\) is \(0.33\), so the area to the left of \(z\) is \(1 - 0.33=0.67\).

Step2: Use the standard normal table (z - table)

Looking up the value in the standard normal table (the cumulative - distribution function of the standard normal distribution \(\varPhi(z)\)). We search for the value closest to \(0.67\) in the body of the z - table.
The standard normal table gives \(z\) values. If we look at the z - table:
The closest value to \(0.67\) in the standard normal table. The row for \(z = 0.4\) and the column for \(0.04\) gives \(\varPhi(0.44)=0.6700\)

Answer:

\(z_{0.33}=0.44\)