for a confidence level of 88%, find the critical value

Explanation:

Step1: Calculate the significance level $\alpha$

$\alpha=1 - 0.88=0.12$

Step2: Find the two - tailed $\alpha/2$ value

$\frac{\alpha}{2}=\frac{0.12}{2}=0.06$

Step3: Look up the $z$ - value in the standard normal distribution table

We want to find $z_{\alpha/2}$ such that $P(Z>z_{\alpha/2}) = 0.06$. Looking up in the standard normal table (or using a calculator with a normal - distribution function), we know that $P(Z\leq z)=1 - 0.06 = 0.94$. The $z$ - value corresponding to a cumulative probability of $0.94$ is approximately $z = 1.555$.

Answer:

$1.555$