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Given a normal distribution with μ = 73 and σ = 12.:
calculate the 68-95-99.7 rule, or three-sigma rule, or empirical rule ranges
Range 1, or the 68% range, states that
68% of the normal distribution values lie within 1 standard deviation of the mean
68% of values are within μ ± σ
μ ± σ = 73 ± 12.
73 - 12. <= 68% of values <= 73 + 12.
61 <= 68% of values <= 85
95% of values are within μ ± 2σ
μ ± 2σ = 73 ± 2(12.)
73 - 2 x 12. <= 95% of values <= 73 + 2 x 12.
73 - 24 <= 95% of values <= 73 + 24
49 <= 95% of values <= 97
Range 3, or the 99.7% range, states that
99.7% (virtually ALL) of the normal distribution values lie within 3 standard deviations of the mean
99.7% of values are within μ ± 3σ
μ ± 3σ = 73 ± 3(12.)
73 - 3 x 12. <= 99.7% of values <= 73 + 3 x 12.
73 - 36 <= 99.7% of values <= 73 + 36