# What's the difference between a binomial, hypergeometric, and Poisson probability distribution?

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The key differences between binomial, hypergeometric, and Poisson probability distributions lie in their underlying assumptions and the types of scenarios they model.

Binomial distribution:

- Models the number of successes in a fixed number of independent Bernoulli trials.
- Assumes a fixed number of trials, each with two possible outcomes (success or failure).
- The probability of success remains constant for each trial.
- Example scenarios include coin flips, where the outcome of each flip is either heads or tails, or counting the number of defective items in a sample of fixed size from a production line.

Hypergeometric distribution:

- Models the number of successes in a sample drawn without replacement from a finite population.
- Assumes a fixed population size, a fixed number of successes in the population, and a fixed sample size.
- The probability of success changes as items are drawn from the population without replacement.
- Example scenarios include drawing cards from a deck without replacement, where the population consists of the total number of cards, and success is defined as drawing a specific type of card (e.g., aces or red cards).

Poisson distribution:

- Models the number of events occurring in a fixed interval of time or space.
- Assumes events occur independently and at a constant average rate.
- There is no upper limit on the number of events that can occur.
- Example scenarios include the number of phone calls received by a call center in an hour, the number of accidents at a particular intersection in a day, or the number of particles emitted by a radioactive source in a given time period.

In summary, the binomial distribution deals with a fixed number of trials with two possible outcomes, the hypergeometric distribution deals with sampling without replacement from a finite population, and the Poisson distribution deals with the number of events occurring in a fixed interval of time or space with a constant average rate.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- The commuting time for all employees of a company has a normal distribution with a mean of 44.6 minutes and a standard deviation of 11.2 minutes. What is the probability that the mean computing time by a sample of 12 employees is between 43.26 and 49.35?
- How do you find the mean of the following set of numbers: 12, 14, 16, 12, 13?
- There are 8 members of the women’s basketball team and 7 members of the men’s track team at an athletic club meeting. What is the probability that a committee of 3 selected at random will have at least 2 members of the basketball team?
- Products from a certain machine are too large 15% of the time. What is the probability that in a run of 20 parts, 5 are too large?
- You keep track of the time you spend doing homework each evening. You spend 58 minutes, 36 minutes, 44 minutes, and 37 minutes. How do you find the mean of these times?

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