Using the 68, 95, and 99.7 empirical rule. What is the probability that a outcome will be between the mean and one standard deviation above the mean?

Answer 1

The 68, 95, and 99.7 empirical rule states the probability that an outcome will be between the mean and one standard deviation above the mean is 68. The empirical rule is a shorthand rule of thumb that allows one to approximate the probability. For example in statistics, despite argumentation among those in the field, it is known that one standard deviation above and below the mean will comprise approximately .6827.

Therefore:

P_r (µ -1σ ≤ X ≤ μ + 1σ) ≈ 0.6827

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