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Chapter 6: Problem 64

Alaska Airlines has an on-time arrival rate of \(88 \%\). Assume that in one day, this airline has 1200 flights. Suppose we pick one day in December and find the number of ontime Alaska Airline arrivals. Why would it be inappropriate to use the binomial model to find the probability that at least 1100 of the 1200 flights arrive on time? What condition or conditions for use of the binomial model is or are not met?

Short Answer

Expert verified
The use of the binomial model is inappropriate in this case because the condition that the probability of 'success' is the same for each outcome is not necessarily met. Variability in factors affecting on-time arrivals (like weather conditions, maintenance issues, air traffic, etc.) means the probability could fluctuate, hence Binomial model is not suitable.

Step by step solution

01

Understand the Situation

The situation here is an airline with 1200 flights a day, with an on-time arrival rate of \(88 \%\). If we are trying to find the probability that at least 1100 of the 1200 flights arrive on time, we should consider four conditions of the Binomial Model.
02

Check Fixed Number of Observations

The first condition for the binomial model to apply is that the number of observations (n) should be fixed. Here, the number of flights per day (1200) is stated, meaning condition one is met.
03

Check Independence of Observations

Second condition is that each observation should be independent. In this case, assuming one flight being on time does not affect the on-time status of another flight, the independence condition is met.
04

Check Two Possible Outcomes

Third condition requires that each observation should represent one of two outcomes ('Success' or 'Failure'). Here, the two possible outcomes are that a flight arrives either on time (success) or not on time (failure). Therefore, the third condition is met.
05

Check Constant Probability

The fourth condition stipulates that the probability of 'success' (p) should be the same for each outcome. Here, since weather conditions, maintenance issues, air traffic control could affect the on-time arrival rate and these conditions vary from day to day, we can't really say that the probability of success is constant. This is where the Binomial model wouldn't be a suitable choice.

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