Question

find the value of $z_{\alpha}$. $z_{0.48}$ click the icon to view a table of areas under the normal curve. $z_{0.48}=\square$ (round to two decimal places as needed.)

Explanation:

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

\(z_{\alpha}\) represents the z - score such that the area to the right of \(z_{\alpha}\) under the standard normal curve is \(\alpha\). Here \(\alpha = 0.48\), so the area to the left of \(z_{0.48}\) is \(1 - 0.48=0.52\)

Step2: Use the standard normal table

Looking up the value \(0.52\) in the standard normal table (z - table). The standard normal table gives the cumulative probability \(P(Z\leq z)\).
We know that for \(z = 0.05\), \(P(Z\leq0.05)=0.5199\approx0.52\)

Answer:

\(0.05\)