Home Â» 5 Real-Life Examples of the Poisson Distribution

# 5 Real-Life Examples of the Poisson Distribution

The Poisson distribution is a probability distribution thatÂ is used to model the probability that a certain number of events occur during a fixed time interval when the events are known to occur independently and with a constant mean rate.

In this article we share 5 examples of how the Poisson distribution is used in the real world.

### Example 1: Calls per Hour at a Call Center

Call centers use the Poisson distribution to model the number of expected calls per hour that theyâ€™ll receive so they know how many call center reps to keep on staff.

For example, suppose a given call center receives 10 calls per hour. We can use a Poisson distribution calculator to find the probability that a call center receives 0, 1, 2, 3 â€¦ calls in a given hour:

• P(X = 0 calls) = 0.00005
• P(X = 1 call) = 0.00045
• P(X = 2 calls) = 0.00227
• P(X = 3 calls) = 0.00757

And so on.

This gives call center managers an idea of how many calls theyâ€™re likely to receive per hour and enables them to manage employee schedules based on the number of expected calls.

### Example 2: Number of Arrivals at a Restaurant

Restaurants use the Poisson distribution to model the number of expected customers that will arrive at the restaurant per day.

For example, suppose a given restaurant receives an average of 100 customers per day. We can use the Poisson distribution calculator to find the probability that the restaurant receives more than a certain number of customers:

• P(X > 110 customers) = 0.14714
• P(X > 120 customers) = 0.02267
• P(X > 130 customers) = 0.00171

And so on.

This gives restaurant managers an idea of the likelihood that theyâ€™ll receive more than a certain number of customers in a given day.

### Example 3: Number of Website Visitors per Hour

Website hosting companies use the Poisson distribution to model the number of expected visitors per hour that websites will receive.

For example, suppose a given website receives an average of 20 visitors per hour. We can use the Poisson distribution calculator to find the probability that the website receives more than a certain number of visitors in a given hour:

• P(X > 25 visitors) = 0.11218
• P(X > 30 visitors) = 0.01347
• P(X > 35 visitors) = 0.00080

And so on.

This gives hosting companies an idea of how much bandwidth to provide to different websites to ensure that theyâ€™ll be able to handle a certain number of visitors each hour.

### Example 4: Number of Bankruptcies Filed per Month

Banks use the Poisson distribution to model the number of expected customer bankruptcies per month.

For example, suppose a given bank has an average of 3 bankruptcies filed by customers each month. We can use the Poisson distribution calculator to find the probability that the bank receives a specific number of bankruptcy files in a given month:

• P(X = 0 bankruptcies) = 0.04979
• P(X = 1 bankruptcy) = 0.14936
• P(X = 2 bankruptcies) = 0.22404

And so on.

This gives banks an idea of how much reserve cash to keep on hand in case a certain number of bankruptcies occur in a given month.

### Example 5: Number of Network Failures per Week

Technology companies use the Poisson distribution to model the number of expected network failures per week.

For example, suppose a given company experiences an average of 1 network failure per week. We can use the Poisson distribution calculator to find the probability that the company experiences a certain number of network failures in a given week:

• P(X = 0 failures) = 0.36788
• P(X = 1 failure) = 0.36788
• P(X = 2 failures) = 0.18394

And so on.

This gives the company an idea of how many failures are likely to occur each week.