Math Problem Statement

A certain airline has 167 seats available for a flight from YYC (Calgary International Airport) to LAX (Los Angeles International Airport). Because people with reservations do not show up for their flight 13% of the time, the airline always overbooks this flight. That is, there are more passengers that have tickets on the flight than there are seats.

Suppose the airline has 179 passengers booked for 167 seats. Assume one person showing up for the flight does not affect others who may, or may not, show up for this flight.

(a) How many people (with tickets) does the airline expect to show up for this flight? Provide the standard deviation as well. Enter your answers to two decimals.

The expectation of the number of people showing up for the flight

The standard deviation of the number of people who show up for the flight

Solution

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Math Problem Analysis

Mathematical Concepts

Binomial Distribution
Probability

Formulas

Expected value of binomial distribution E(X) = n * p
Standard deviation of binomial distribution σ = sqrt(n * p * (1 - p))

Theorems

Binomial Theorem

Suitable Grade Level

College level, Statistics/Probability