Answer:Given a normal distribution with μ = 62 and σ = 4., 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 = 62 ± 4.
62 - 4. <= 68% of values <= 62 + 4.
58 <= 68% of values <= 66
Calculate Range 2:
Range 2, or the 95% range, states that 95% of the normal distribution values lie within 2 standard deviations of the mean
95% of values are within μ ± 2σ
μ ± 2σ = 62 ± 2(4.)
62 - 2 x 4. <= 95% of values <= 62 + 2 x 4.
62 - 8 <= 95% of values <= 62 + 8
54 <= 95% of values <= 70
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 = 62 ± 3(4.)
62 - 3 x 4. <= 99.7% of values <= 62 + 3 x 4.
62 - 12 <= 99.7% of values <= 62 + 12
50 <= 99.7% of values <= 74
Step-by-step explanation:
