when finding the margin of error for the mean of a normally distributed population from a sample, what is…

Explanation:

Step1: Recall the relationship between confidence - level and critical probability

The confidence level $C$ and the critical probability $\alpha/2$ are related. The total area under the normal - distribution curve is 1. The confidence level $C$ is the area in the middle of the distribution, and the remaining area in the two tails is $1 - C$. The critical probability $\alpha/2$ is the area in one of the tails.

Step2: Calculate the area in the two tails

Given a confidence level $C = 0.58$. The area in the two tails is $1 - C=1 - 0.58 = 0.42$.

Step3: Calculate the critical probability

Since the distribution is symmetric, the area in one tail (the critical probability $\alpha/2$) is $\frac{1 - C}{2}$. Substituting $1 - C = 0.42$ into the formula, we get $\frac{0.42}{2}=0.21$.

Answer:

0.21