Math Problem Statement

A survey found that​ women's heights are normally distributed with mean 63.2 in. and standard deviation 2.9 in. The survey also found that​ men's heights are normally distributed with mean 67.6 in. and standard deviation 3.1 in. Most of the live characters employed at an amusement park have height requirements of a minimum of 56 in. and a maximum of 63 in. Complete parts​ (a) and​ (b) below. If the height requirements are changed to exclude only the tallest​ 50% of men and the shortest​ 5% of​ men, what are the new height​ requirements?

Solution

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Math Problem Analysis

Mathematical Concepts

Normal Distribution
Percentiles
Z-scores

Formulas

z = (X - μ) / σ

Theorems

Standard Normal Distribution
Percentile Calculation Using Z-scores

Suitable Grade Level

Grades 11-12