# Poisson Distribution Statistics

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In summary, Poisson Distribution is a probability distribution used to model the number of times an event occurs in a given time period. It has three main assumptions, including a constant probability of an event occurring and independence of events. The mean and variance can be calculated using the formula λ = np, with the standard deviation being the square root of the mean. Poisson Distribution differs from Normal Distribution in that it is used for discrete data and rare events, while Normal Distribution is used for continuous data and a wider range of data. Poisson Distribution has various real-life applications, such as in finance, insurance, and biology, to model events like customer arrivals, insurance claims, and mutations in a DNA sequence.
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## Homework Statement

If the number of complaints a dry cleaning establishment receives per day is random variable having the Poisson distribution with λ = 3.3, what are the probabilities that it will receive:

(a) Five complaints altogether on any two given days.

(b) at least 12 complaints altogether on any 3 given days.

## Homework Equations

Poisson Distribution

## The Attempt at a Solution

Please show us your best attempt so far so we can understand how you are thinking about the problem and where you get stuck. Thanks.

## What is Poisson Distribution?

Poisson Distribution is a probability distribution that is used to model the number of times an event occurs in a given time period. It is often used to calculate the likelihood of rare events, such as the number of customers arriving at a store in a given hour or the number of accidents on a highway in a day.

## What are the assumptions for using Poisson Distribution?

There are three main assumptions for using Poisson Distribution: 1) The probability of an event occurring in a given time interval is constant. 2) The events are independent of each other. 3) The events cannot occur more than once within a given time interval.

## How do you calculate the mean and variance for Poisson Distribution?

The mean and variance for Poisson Distribution are equal and can be calculated using the formula: λ = np, where λ (lambda) is the mean and p is the probability of an event occurring. The standard deviation can be calculated as the square root of the mean (or variance).

## What is the difference between Poisson Distribution and Normal Distribution?

Poisson Distribution is used for discrete data, while Normal Distribution is used for continuous data. Poisson Distribution is used to model rare events, while Normal Distribution is used to model a wide range of data. Additionally, the shape of the curves for the two distributions is different, with Poisson Distribution being skewed to the right and Normal Distribution being symmetric.

## How do you use Poisson Distribution in real-life applications?

Poisson Distribution is commonly used in various fields, such as finance, insurance, and telecommunications, to model events such as customer arrivals, insurance claims, and network failures. It is also used in biology to model the number of mutations in a DNA sequence and in sports to model the number of goals scored in a game.

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