Math Problem Statement
In a survey of
11511151
people,
782782
people said they voted in a recent presidential election. Voting records show that
6565%
of eligible voters actually did vote. Given that
6565%
of eligible voters actually did vote, (a) find the probability that among
11511151
randomly selected voters, at least
782782
actually did vote. (b) What do the results from part (a) suggest?
Question content area bottom
Part 1
(a)
P(Xgreater than or equals≥782782)equals=
Solution
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Math Problem Analysis
Mathematical Concepts
Probability Theory
Binomial Distribution
Normal Approximation
Z-scores
Formulas
P(X ≥ x) = 1 - P(X < x) (Probability of at least x successes)
μ = np (Mean of binomial distribution)
σ = √(np(1 - p)) (Standard deviation of binomial distribution)
z = (X - μ) / σ (Z-score for normal approximation)
Theorems
Central Limit Theorem
Normal Approximation to the Binomial Distribution
Suitable Grade Level
Grades 11-12, College Introductory Statistics
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