Binomial Distribution - Assumptions

In summary, the assumption that must be made in using a binomial distribution to model the situation is that each passenger's decision to book and show up is independent of the other passengers' decisions. This assumption may not be completely reasonable as there could be external factors that affect each passenger's decision.
  • #1
Peter G.
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Hi,

An airline knows from past experience that the probability of a person booking a seat and then not turning up is 0.04. A small plane has 50 seats and 55 bookings are made.

a) A binomial distribution is used to model this situation. What assumption must be made? Comment on how reasonable this assumption must be made

I really don't know how to answer this, due to the fact my book does not give me much information on Binomial Distribution, just several examples. The only restriction I know of is that there must be Yes and No experiments. In that case, the assumption here would be that no passenger does not book and show up...

Can anyone give me any tips?

Thanks,
Peter G.
 
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  • #2
Peter G. said:
Hi,

An airline knows from past experience that the probability of a person booking a seat and then not turning up is 0.04. A small plane has 50 seats and 55 bookings are made.

a) A binomial distribution is used to model this situation. What assumption must be made? Comment on how reasonable this assumption must be made

I really don't know how to answer this, due to the fact my book does not give me much information on Binomial Distribution, just several examples. The only restriction I know of is that there must be Yes and No experiments. In that case, the assumption here would be that no passenger does not book and show up...

Can anyone give me any tips?

Thanks,
Peter G.

The binomial distribution is about repeated trials. But look again in your text. You will find an adjective modifying the word trials.
 

1. What are the key assumptions of binomial distribution?

The key assumptions of binomial distribution include: (1) a fixed number of trials or observations, (2) each trial has only two possible outcomes (success or failure), (3) the probability of success remains constant for each trial, and (4) the trials are independent of each other.

2. Can binomial distribution be applied to continuous data?

No, binomial distribution is only applicable to discrete data where the outcomes are mutually exclusive and the probability of success is constant for each trial.

3. What is the relationship between binomial distribution and normal distribution?

Binomial distribution can be approximated by normal distribution when the number of trials is large (n ≥ 30) and the probability of success is not too close to 0 or 1 (0.1 ≤ p ≤ 0.9). This approximation is known as the central limit theorem.

4. Are there any limitations to using binomial distribution?

Yes, binomial distribution assumes that the trials are independent of each other, which may not always be true in real-world situations. It also assumes a fixed number of trials, which may not always be known or may change over time.

5. What are some real-world applications of binomial distribution?

Binomial distribution is commonly used in fields such as statistics, genetics, and psychology to model and analyze data related to binary outcomes. Some examples include market research surveys, opinion polls, and genetics studies on genetic traits.

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