Question

math 21
notes
date:
according to flightstats.com, american airlines flights from dallas to chicago are on time 80% of the time. suppose 24 flights are randomly selected, and the number of on - time flights is recorded.
a. explain why this is a binomial experiment.
b. determine the values of n, p, q, and x.

Explanation:

Part a

A binomial experiment has the following characteristics:

• Fixed number of trials: Here, \(n = 24\) flights are selected (fixed number of trials).
• Two - outcome per trial: A flight is either on - time (success) or not on - time (failure).
• Independent trials: The on - time status of one flight is assumed to be independent of another flight's on - time status.
• Constant probability of success: The probability \(p\) that a flight is on - time is \(p=0.8\) (constant for all trials)

Part b

• \(n\) (number of trials): The number of flights selected is \(n = 24\)
• \(p\) (probability of success): The probability that a flight is on - time is \(p = 0.8\)
• \(q\) (probability of failure): Since \(q=1 - p\), then \(q=1 - 0.8=0.2\)
• \(x\) (number of successes in \(n\) trials): \(x\) represents the number of on - time flights among the \(24\) selected flights. So \(x = 0,1,\cdots,24\)

Answer:

Part a

This is a binomial experiment because there is a fixed number of trials (\(n = 24\) flights), each trial has two outcomes (on - time or not on - time), the trials are independent (on - time status of one flight does not affect another), and the probability of success (a flight being on - time, \(p = 0.8\)) is constant.

Part b

\(n = 24\), \(p=0.8\), \(q = 0.2\), \(x\in\{0,1,\cdots,24\}\)