Question
Asked Dec 8, 2019
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Suppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.11 and a standard deviation of 1.46 Using the empirical rule, what percentage of American women have shoe sizes that are at least 11.03? Please do not round your answer.

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Expert Answer

Step 1

Consider,

X be a random variable that represents the shoe size of American women that has a bell-shaded distribution.

Mean (µ) = 8.11

Standard deviation (σ) =1.46

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The empirical rule has the following properties, Property 1: Approximately 68% of the data values fall within one standard deviation of mean, that is. (u-10,u+l0). Property 2: Approximately 95% of the data values fall within two standard deviations of mean, that is , (μ-2σ, μ + 2σ). Property 3: Approximately 99.7% of the data values fall within three standard deviations of mean, that is , ( μ-3σ, μ + 3σ).

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Step 2

Thus,

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1. (8.11-1x1.46,8.11+1×1.46)= 0.68 (6.65,9.57) = 0.68 2. (8.11–2x1.46,8.11+2×1.46) = 0.95 (5.19,11.03) = 0.95 3. (8.11–3×1.46,8.11+3×1.46) = 0.99 (3.73,12.49) = 0.99

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Step 3

Hence, the percentage of shoe size that are at lea...

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.: (5.19,11.03) = 0.95 P(X 211.03) - 0.025

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