Question

compute the critical value ( z_{alpha / 2} ) that corresponds to a ( 87% ) level of confidence
click here to view the standard normal distribution table (page 1).
click here to view the standard normal distribution table (page 2).
( z_{alpha / 2}=square )
(round to two decimal places as needed)

Explanation:

Step1: Calculate the significance level $\alpha$

The confidence level is \(C = 87\%=0.87\). Using the formula \(\alpha=1 - C\), we get \(\alpha=1 - 0.87 = 0.13\).

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

\(\frac{\alpha}{2}=\frac{0.13}{2}=0.065\).

Step3: Find the \(z\) - value

We want to find \(z_{\alpha/2}\) such that \(P(Z>z_{\alpha/2})=\frac{\alpha}{2}=0.065\), or equivalently \(P(Z\leq z_{\alpha/2})=1 - 0.065 = 0.935\).
Looking up in the standard - normal distribution table (the \(z\) - table), we find that the \(z\) - value corresponding to a cumulative probability of \(0.935\) is \(z = 1.51\) (by interpolation or using a more accurate table/technology).

Answer:

\(1.51\)