# POISSON.DIST

The `POISSON.DIST` function calculates the Poisson distribution, which is a statistical distribution that shows how many times an event is likely to occur within a specified period of time, given the average rate of occurrence. This function is commonly used in probability theory to model the number of times an event occurs in a fixed interval of time or space. The resulting value represents the probability of the event occurring a certain number of times. If the cumulative argument is set to TRUE (or omitted), the function returns the cumulative distribution function; if set to FALSE, it returns the probability density function.

## Usage

Use the `POISSON.DIST` formula with the syntax shown below, it has 2 required parameters and 1 optional parameter:

Parameters:
1. x (required):
The number of events that you want to find the probability for.
2. mean (required):
The average rate of occurrence of the event per interval.
3. cumulative (optional):
An optional boolean value that determines the form of the function. If set to TRUE or omitted, the function returns the cumulative distribution function; if set to FALSE, it returns the probability density function.

## Examples

Here are a few example use cases that explain how to use the `POISSON.DIST` formula in Google Sheets.

### Calculating the probability of a certain number of events occurring

Suppose you want to find the probability that a certain number of customers will visit your store during a given hour, knowing that the average rate of customer arrivals is 10 per hour. You can use the `POISSON.DIST` function to calculate this probability.

### Modeling the number of defects in a manufacturing process

A manufacturer produces items with a known average rate of defects per unit. By applying the Poisson distribution, the manufacturer can estimate the likelihood of a certain number of defects in a given number of units produced.

### Predicting website traffic

A website owner can use the Poisson distribution to predict the number of visitors to their site in a given time period based on historical data on visitor arrivals.

## Common Mistakes

`POISSON.DIST` not working? Here are some common mistakes people make when using the `POISSON.DIST` Google Sheets Formula:

### Misunderstanding the mean parameter

One common mistake is to use the actual number of events instead of the expected number of events as the mean parameter. The mean parameter represents the average number of events over a specified period of time, not the actual number of events in a single sample.

### Forgetting to specify the cumulative parameter

Another common mistake is to omit the cumulative parameter when calculating the cumulative distribution function. If the cumulative parameter is not specified, the function will return the probability density function.

The following functions are similar to `POISSON.DIST` or are often used with it in a formula:

• `POISSON`

The `POISSON` function returns the Poisson distribution probability density function, which is used to show the probability of a certain number of events occurring in a fixed interval of time or space. It takes in the values for the number of events (x), the mean (mean), and a boolean for whether or not to return the cumulative distribution (cumulative).

• `BINOM.DIST`

The `BINOM.DIST` function returns the probability of a certain number of successes in a fixed number of trials given a probability of success in each trial. It is most commonly used in statistical analysis and hypothesis testing. The function can calculate either the probability mass function (PMF) or the cumulative distribution function (CDF) depending on the value of the `cumulative` parameter.

• `NORM.DIST`

The `NORM.DIST` formula is a statistical function that returns the normal distribution of a specified variable. It is used to determine the probability of a random variable falling within a specified range of values. This function is commonly used in finance and scientific research.

• `TDIST`

The `TDIST` function calculates the probability associated with a Student's t-Test. It returns the probability that the difference between two data sets is greater than or equal to a certain value. This function is commonly used in hypothesis testing.

• `CHISQ.DIST`

The `CHISQ.DIST` function calculates the probability density function or the cumulative distribution function of a chi-squared distribution. This function is commonly used in hypothesis testing to determine the significance of the difference between expected and observed values. The output of this function can be used to make decisions about the null hypothesis.

You can learn more about the `POISSON.DIST` Google Sheets function on Google Support.