Respuesta :
The mean is 65 inches and the standard deviation is 3 inches.
Given,
In a group of women, the distribution of heights is roughly normal. Women who are shorter than 62 inches in height make up 16% of the population.
The empirical rule, less than μ - σ of 16% of the data is accurate.
P (x < μ - σ) = 16%
μ - σ = 62 → (I)
Approximately 97.5% of the women are under 71 inches in height,
P (x < μ + 2σ) = 97.5%
μ + 2σ = 71 → (II)
By solving (I) & (II);
μ - σ = 62
μ + 2σ = 71
3σ = 9
σ = 3
From (I);
μ - σ = 62
μ - 3 = 62
μ = 65
Hence, Mean = 65 inches
Standard deviation = 3 inches
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