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(a) 68% of the data
______ cm — ______ cm
(b) 95% of the data
______ cm — ______ cm
(c) 99.7% of the data
_______cm — _______ cm
Solution
Given: normal distribution, μ = 177 cm, σ = 7.4 cm
In a normal distribution: 68% of the data lies between μ-1σ and μ+1σ
μ-1σ = 177 – 7.4 = 169.6 cm; μ+1σ = 177 + 7.4 = 184.4 cm
a) 68%: 169.6 cm – 184.4 cm
In a normal distribution: 95% of the data lies between μ-2σ and μ+2σ
μ-2σ = 177 – 2(7.4) = 162.2 cm; μ+2σ = 177 + 2(7.4) = 191.8 cm
b) 98%: 162.2 cm – 191.8 cm
In a normal distribution: 99.7% of the data lies between μ-3σ and μ+3σ
μ-23σ = 177 – 3(7.4) = 154.8 cm; μ+3σ = 177 + 3(7.4) = 199.2 cm
c) 99.7%: 154.8 cm – 199.2 cm