Question

find the indicated critical value.
$z_{0.05}$
$z_{0.05}=\square$
(round to three decimal places as needed.)

Explanation:

Step1: Understand the critical value notation

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, \( \alpha = 0.05 \).

Step2: Use the property of the standard normal distribution

We know that the total area under the standard normal curve is \( 1 \). If the area to the right of \( z_{0.05} \) is \( 0.05 \), then the area to the left of \( z_{0.05} \) is \( 1-\alpha=1 - 0.05=0.95 \).

Step3: Look up the z - score in the standard normal table (or use a calculator with a normal - distribution function)

Using a standard normal table (or a calculator, for example, in Excel the function is \(=\text{NORM.S.INV}(0.95)\)), we find the z - score.

Answer:

\( 1.645 \)