POISSON.DIST
The POISSON.DIST function calculates the Poisson probability mass function. It represents the probability of a given number of events occurring in a fixed interval. Events occur with a known constant mean rate and independently of the time since the last event.
Syntax 🔗
=POISSON.DIST(x, mean, cumulative)
x | The number of events that you want to find the probability mass function value for. |
mean | The average rate of events occurring. |
cumulative | A logical value that determines the form of the function. TRUE for the cumulative distribution function, FALSE for the probability mass function. Default is FALSE. |
About POISSON.DIST 🔗
Use the POISSON.DIST function in Excel to evaluate the probability of a specific number of events occurring within a given time or space interval. This function is ideal when events follow a Poisson distribution, characterized by a constant mean rate and independent occurrences. It is commonly applied to model situations such as customer arrivals, system failures, or radioactive decay events. With POISSON.DIST, you can calculate the probability mass or cumulative distribution function, helping you make informed decisions based on expected occurrences.
Examples 🔗
Suppose the average number of emails received per day is 20. You want to know the probability of receiving exactly 15 emails in a day. Use the formula: =POISSON.DIST(15, 20, FALSE) This will provide the probability of exactly 15 emails being received in a day.
Suppose in a factory, on average, there are 4 defective products per hour. You are interested in the cumulative probability of having 0 to 2 defective products in 1 hour. Use the formula: =POISSON.DIST(2, 4, TRUE) - POISSON.DIST(0, 4, TRUE) This will give the cumulative probability of having 0 to 2 defects per hour.
Notes 🔗
Ensure that both the mean and x values are non-negative. The POISSON.DIST function relies on the Poisson probability mass function, which assumes that events occur independently and at a constant mean rate. Be aware of these assumptions before using this function in real-world applications.
Questions 🔗
The mean parameter in the POISSON.DIST function indicates the average rate at which events occur. It helps define the Poisson distribution and is crucial for calculating the probabilities of different event occurrences.
How does the cumulative parameter affect the output of the POISSON.DIST function?The cumulative parameter in the POISSON.DIST function determines whether you are calculating the probability mass function (FALSE) or the cumulative distribution function (TRUE). By setting cumulative to TRUE, you get the probability of x or fewer events occurring. Setting it to FALSE provides the probability of exactly x events.
Can the POISSON.DIST function be used for scenarios outside the Poisson distribution assumptions?No, the POISSON.DIST function is specifically designed for scenarios where event occurrences follow a Poisson distribution pattern with independence and constant mean rate. It may not provide accurate results for scenarios that deviate significantly from these assumptions.