The heights of American adult males are normally distributed with a me

krypsojx

krypsojx

Answered question

2021-11-28

The heights of American adult males are normally distributed with a mean of 177 cm and a standard deviation of 7.4 cm. Use the Empirical Rule to find the range of heights that contain approximately
(a) 68% of the data
? cm ? cm
(b) 95% of the data
? cm ?cm
(c) 99.7% of the data
? cm ? cm

Answer & Explanation

Linda Tincher

Linda Tincher

Beginner2021-11-29Added 14 answers

Step 1
Empirical Rule:
- 68% of the observations lies between one standard deviation from the mean.
- 95% of the observations lies between two standard deviations from the mean.
- 99.7% of the observations lies between three standard deviations from the mean.
Given:
μ=177
σ=7.4
a)(μσ,μ+σ)=(1777.4,177+7.4)=(169.6,184.4)
68% of the data lies between 169.6 cm and 184.4 cm
Step 2
b) (μ2σ,μ+2σ)=(17727.4,177+27.4)=(162.2,191.8)
95% of the data lies between 162.2 cm and 191.8 cm
c) (μ3σ,μ+3σ)=(17737.4,177+37.4)=(154.8,199.2)
99.7% of the data lies between 154.8 cm and 199.2 cm

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