Question

find the indicated value.

$z_{0.09}$

1.6954
1.3408
0.9154
0.6128

Explanation:

Step1: Understand the notation

\(z_{\alpha}\) represents the \(z -\)score such that the area to the right of \(z_{\alpha}\) under the standard normal curve is \(\alpha\). Here \(\alpha = 0.09\).

Step2: Use the property of the standard normal distribution

The total area under the standard normal curve is \(1\). The area to the left of \(z_{0.09}\) is \(1-\alpha=1 - 0.09=0.91\).

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

We look for the value in the body of the standard - normal table (which gives the cumulative probability \(P(Z\leq z)\)) closest to \(0.91\).
In the standard - normal table, when we look for a cumulative probability of \(0.91\), the corresponding \(z -\)score is approximately \(z = 1.34\).
The more accurate value (using more precise tables or a calculator with a normal - distribution function, e.g., in Excel: =NORM.S.INV(1 - 0.09) or in R: qnorm(0.91)), we get \(z_{0.09}\approx1.3408\).

Answer:

B. \(1.3408\)