Math Problem Statement

High blood pressure has been identified as a risk factor for heart attacks and strokes. The proportion of U.S. adults with high blood pressure is 0.4 . A sample of 40 U.S. adults is chosen. Use the TI-84 Plus calculator as needed. Round the answers to at least four decimal places as needed. Find the probability that more than 42% of the people in this sample have high blood pressure.

Solution

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Math Problem Analysis

Mathematical Concepts

Binomial Distribution
Normal Approximation
Z-scores
Probability

Formulas

Mean of sample proportion: μ_\hat{p} = p
Standard deviation of sample proportion: σ_\hat{p} = √(p(1-p)/n)
Z-score: z = (\hat{p} - μ_\hat{p}) / σ_\hat{p}

Theorems

Central Limit Theorem
Normal Approximation to Binomial Distribution

Suitable Grade Level

College-level Statistics