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 0.3. A sample of 32 U.S. adults is chosen. Use the TI-84 Plus Calculator as needed. Round the answer to at least four decimal places. Find the probability that less than 23% of the people in the sample of 78 have high blood pressure. The probability that less than 23% of the people in the sample of 78 have high blood pressure is
Solution
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Math Problem Analysis
Mathematical Concepts
Statistics
Probability
Binomial Distribution
Normal Approximation
Z-Score
Formulas
Mean of sample proportion: μ_p̂ = p
Standard deviation of sample proportion: σ_p̂ = sqrt[(p(1 - p)) / n]
Z-score formula: z = (p̂ - μ_p̂) / σ_p̂
Theorems
Central Limit Theorem
Normal Approximation to Binomial Distribution
Suitable Grade Level
Grades 10-12
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