Math Problem Statement

The results of a study showed that heterosexual​ women, during​ ovulation, were significantly better at correctly identifying the sexual orientation of a man from a photograph of his face than women who were not ovulating. Near​ ovulation, on average women correctly identified the orientation of about 67​% of the 100 men shown to them. Assume that the sample distribution for this study is unimodal and symmetric and that the samples are collected randomly. If this is the probability of correctly identifying the orientation of a man in any given​ photograph, what is the probability a woman would correctly classify 77 or more of the​ men?

Solution

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Math Problem Analysis

Mathematical Concepts

Binomial Distribution
Normal Approximation
Probability
Z-Scores

Formulas

Mean μ = n * p
Standard Deviation σ = √(n * p * (1 - p))
Z-score z = (X - μ) / σ

Theorems

Normal Approximation to the Binomial Distribution
Central Limit Theorem

Suitable Grade Level

Grades 10-12