Math Problem Statement

Find the indicated probability. Round to three decimal places.8)An airline estimates that97% of people booked on their flights actually show up. If the airlinebooks70people on a flight for which the maximum number is68, what is the probability that thenumber of people who show up will exceed the capacity of the plane?

Solution

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Math Problem Analysis

Mathematical Concepts

Probability
Binomial Distribution
Normal Approximation

Formulas

Binomial probability formula: P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
Normal approximation to binomial: Z = (X - μ) / σ
Mean: μ = np
Standard deviation: σ = √(np(1 - p))

Theorems

Central Limit Theorem

Suitable Grade Level

Grades 11-12