When finding the margin of error for the mean of a normally distributed population from a sample, what is the critical probability, assuming a confidence level of 58 percent ?

A 58% confidence level leaves 1 − 0.58 = 0.42 outside the confidence interval, split equally between the two tails. The cumulative probability to the left of the positive critical value is 1 − 0.42/2 = 0.79, so the critical probability is 0.79.

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