Question

Suppose that, based on a sample, the 99.7% confidence interval for the mean of a population is (59,95). What is the mean of the sample?

Answer 1

Based on a sample where the 99.7% confidence interval for the mean of a population is (59,95), 77 is the mean

Answer 2

mean = 77

Explanation:

We have a confidence interval of (59, 95) with a confidence of 99.7 percent

99.7 is 6 standard deviations from the mean, 3 on each side of the mean

mean - 3 sigma = 59

mean + 3 sigma = 95

We can use elimination to eliminate sigma. Add these equations together

mean - 3 sigma = 59

mean + 3 sigma = 95

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2 * mean = 154

Divide each side by 2

2 * mean/2 = 154/2

mean = 77