Question

find the critical value ( z_{alpha / 2} ) that corresponds to the given confidence level.
91%
( z_{alpha / 2}=square ) (round to two decimal plades as needed.)

Explanation:

Step1: Calculate $\alpha$

The confidence level is \(C = 0.91\). We know that \(\alpha=1 - C\). So, \(\alpha=1 - 0.91=0.09\).

Step2: Calculate \(\frac{\alpha}{2}\)

\(\frac{\alpha}{2}=\frac{0.09}{2}=0.045\).

Step3: Find the \(z\) - value

We want to find \(z_{\alpha/2}\) such that \(P(Z>z_{\alpha/2})=\frac{\alpha}{2}=0.045\), or equivalently \(P(Z\leq z_{\alpha/2})=1 - 0.045 = 0.955\).
Looking up in the standard normal distribution table (or using a calculator with a normal - distribution function, e.g., for a TI - 84: invNorm(0.955)), we get \(z_{\alpha/2}\approx1.70\).

Answer:

\(1.70\)