The heights of American adult males are normally distributed with a mean of 177 cm and a standard deviation of 7.4 cm. Find the range of heights that contain approximately

Question

(a) 68% of the data

______ cm -- ______ cm

(b) 95% of the data

______ cm -- ______ cm

(c) 99.7% of the data

_______cm -- _______ cm

Answer 1

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