Math Problem Statement
53% of all Americans are home owners. If 30 Americans are randomly selected, find the probability that
a. Exactly 15 of them are are home owners. b. At most 16 of them are are home owners. c. At least 17 of them are home owners. d. Between 11 and 19 (including 11 and 19) of them are home owners.
Solution
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Math Problem Analysis
Mathematical Concepts
Probability
Binomial Distribution
Cumulative Probability
Complement Rule
Formulas
P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)
P(X ≤ k) = Σ(P(X = i)) for i = 0 to k
P(X ≥ k) = 1 - P(X ≤ k-1)
Theorems
Binomial Theorem
Complement Rule
Suitable Grade Level
Grades 11-12
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