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Answer

↓Steps Explained:↓

Given a normal distribution with μ = 100 and σ = 15:

calculate the 68-95-99.7 rule, or three-sigma rule, or empirical rule ranges

Calculate Range 1:

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 = 100 ± 15

100 - 15 <= 68% of values <= 100 + 15

85 <= 68% of values <= 115

Calculate Range 2:

95% of values are within μ ± 2σ

μ ± 2σ = 100 ± 2(15)

100 - 2 x 15 <= 95% of values <= 100 + 2 x 15

100 - 30 <= 95% of values <= 100 + 30

70 <= 95% of values <= 130

Calculate Range 3:

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 = 100 ± 3(15)

100 - 3 x 15 <= 99.7% of values <= 100 + 3 x 15

100 - 45 <= 99.7% of values <= 100 + 45

Final Answer