Question

find the value of ( z_{alpha} ).
( z_{0.39} )
( z_{0.39}=square ) (round to two decimal places as needed.)

Explanation:

Step1: Recall the definition 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 \(\alpha\). So for \(z_{0.39}\), the area to the right of \(z_{0.39}\) is \(0.39\), and the area to the left of \(z_{0.39}\) is \(1 - 0.39=0.61\).

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

Look up the value \(0.61\) in the body of the standard normal table. The standard normal table gives the cumulative probability \(P(Z\leq z)\).
The closest value to \(0.61\) in the standard normal table:
If we look at the \(z -\)table, for \(z = 0.28\), \(P(Z\leq0.28)=0.6103\)

Answer:

\(z_{0.39}=0.28\)