# POISSON.DIST Function in Excel

Part 1: Introduce

πΉ Definition: The `POISSON.DIST` function in Microsoft Excel calculates the Poisson distribution, which measures how often an event is likely to occur within a specified period.

πΉ Purpose: It’s used to predict the probability of certain events when you know the average number of times the event has occurred. It’s beneficial for rare events in large datasets.

πΉ Syntax & Arguments:

syntax
`POISSON.DIST(x, mean, cumulative) `

πΉ Explain the Arguments in the function:

• `x`: The actual number of events.
• `mean`: The average number of times the event occurs over a specified period.
• `cumulative`: A logical value; TRUE returns the cumulative distribution function; FALSE returns the probability mass function.

πΉ Return value: This function returns the Poisson distribution probability.

πΉ Remarks: The `POISSON.DIST` function can be used for rare events, given a large sample size. Ensure that the mean is a positive number.

Part 2: Examples

π Example 1:

β’ Purpose of example: Determine the probability of receiving exactly 3 customer complaints daily when the average number of complaints is 2.

β’ Data tables and formulas:

ABCD
1xMeanCumulativeResult
232FALSE=POISSON.DIST(A2,B2,C2)
30.180

β’ Explanation: Given an average of 2 complaints per day, the probability of receiving exactly 3 complaints on a particular day is 18.0%.

π Example 2:

β’ Purpose of example: Determine the cumulative probability of receiving up to 4 faulty products in a shipment when the average number of defective products is 3.

β’ Data tables and formulas:

ABCD
1xMeanCumulativeResult
243TRUE=POISSON.DIST(A2,B2,C2)
30.647

β’ Explanation: Given an average of 3 faulty products per shipment, the cumulative probability of receiving up to 4 faulty products is 64.7%.

π Example 3:

β’ Purpose of example: Determine the probability of a website receiving precisely 10 hits in an hour when the average number of hits per hour is 8.

β’ Data tables and formulas:

ABCD
1xMeanCumulativeResult
2108FALSE=POISSON.DIST(A2,B2,C2)
30.112

β’ Explanation: Given an average of 8 website hits per hour, the probability of receiving exactly 10 hits per hour is 11.2%.

π Example 4:

β’ Purpose of example: Determine the cumulative probability of a call center receiving up to 5 calls in 10 minutes when the average number of calls per 10 minutes is 4.

β’ Data tables and formulas:

ABCD
1xMeanCumulativeResult
254TRUE=POISSON.DIST(A2,B2,C2)
30.785

β’ Explanation: Given an average of 4 calls every 10 minutes, the cumulative probability of receiving up to 5 calls in that time frame is 78.5%.

π Example 5:

β’ Purpose of example: Determine the probability of a factory producing exactly 7 defective items daily when the average number of faulty items made daily is 5.

β’ Data tables and formulas:

ABCD
1xMeanCumulativeResult
275FALSE=POISSON.DIST(A2,B2,C2)
30.104

β’ Explanation: Given an average production of 5 defective items daily, the probability of the factory producing exactly 7 defective items on a particular day is 10.4%.

π Example 6: Using POISSON.DIST with IF

β’ Purpose of example: Determine if a server faces 15 requests per minute on average and is under unusual load if it receives 25 recommendations in a minute.

β’ Data tables and formulas:

ABCDE
1xMeanCumulativeFormulaResult
22515TRUE=IF(POISSON.DIST(A2,B2,C2)>0.95, “Unusual”, “Normal”)Unusual

β’ Explanation: If the cumulative probability of receiving 25 or fewer requests is greater than 95%, it’s considered unusual. In this case, the server receiving 25 recommendations in a minute is deemed unique.

π Example 7: Using POISSON.DIST with SUM

β’ Purpose of example: Calculate the combined probability of a bookstore selling 2, 3, or 4 rare books daily when the average sale is 3 rare books daily.

β’ Data tables and formulas:

ABCDE
1xMeanCumulativeFormulaResult
223FALSE=SUM(POISSON.DIST(A2,B2,C2), POISSON.DIST(A3,B3,C3), POISSON.DIST(A4,B4,C4))0.647
333FALSE
443FALSE

β’ Explanation: The individual probabilities of selling 2, 3, or 4 rare books are summed up to get a combined probability. The combined chance of selling 2 to 4 rare books daily is 64.7%.

π Example 8: Using POISSON.DIST with VLOOKUP

β’ Purpose of example: Given a table of average sales, determine the probability of selling 5 products of a specific type per day.

β’ Data tables and formulas:

ABCDE
1Product TypexCumulativeFormulaResult
2Type A5FALSE=POISSON.DIST(B2,VLOOKUP(A2,F:G,2,FALSE),C2)0.175
3

Average Sales Table:

FG
1Product TypeAverage Sales
2Type A4
3Type B6

β’ Explanation: The `VLOOKUP` function fetches the average “Type A” sales from the Average Sales Table. The `POISSON.DIST` function then calculates the probability of selling exactly 5 “Type A” products in a day. The result is a 17.5% chance.

π Example 9: Using POISSON.DIST with AVERAGE

β’ Purpose of example: Calculate the average probability of a bakery selling 3, 4, or 5 pastries in an hour when the average sale is 4 pastries per hour.

β’ Data tables and formulas:

ABCDE
1xMeanCumulativeFormulaResult
234FALSE=AVERAGE(POISSON.DIST(A2,B2,C2), POISSON.DIST(A3,B3,C3), POISSON.DIST(A4,B4,C4))0.238
344FALSE
454FALSE

β’ Explanation: The individual probabilities of selling 3, 4, or 5 pastries are averaged. The average probability of selling between 3 to 5 pastries in an hour, given an average sale of 4 pastries, is 23.8%.

π Example 10: Using POISSON.DIST with MAX

β’ Purpose of example: Determine the highest probability of a website receiving 10, 11, or 12 visitors in an hour when the average number of visitors is 10.

β’ Data tables and formulas:

ABCDE
1xMeanCumulativeFormulaResult
21010FALSE=MAX(POISSON.DIST(A2,B2,C2), POISSON.DIST(A3,B3,C3), POISSON.DIST(A4,B4,C4))0.125
31110FALSE
41210FALSE

β’ Explanation: The `MAX` function is used to determine the highest probability among the three scenarios. The highest probability is for the website to receive precisely 10 visitors in an hour, which is 12.5%.

π Example 11: Using POISSON.DIST with MIN

β’ Purpose of example: Determine the lowest probability of a call center receiving 6, 7, or 8 calls in 10 minutes when the average number is 7.

β’ Data tables and formulas:

ABCDE
1xMeanCumulativeFormulaResult
267FALSE=MIN(POISSON.DIST(A2,B2,C2), POISSON.DIST(A3,B3,C3), POISSON.DIST(A4,B4,C4))0.137
377FALSE
487FALSE

β’ Explanation: The `MIN` function is used to determine the lowest probability among the three scenarios. The lowest probability is for the call center to receive 6 calls in 10 minutes, which is 13.7%.

π Example 12: Using POISSON.DIST with ROUND

β’ Purpose of example: Calculate the rounded probability of a factory producing 5 defective items daily when the average number of faulty items is 4.

β’ Data tables and formulas:

ABCDE
1xMeanCumulativeFormulaResult
254FALSE=ROUND(POISSON.DIST(A2,B2,C2), 3)0.157

β’ Explanation: The `ROUND` function is used to round the result of the `POISSON.DIST` function to three decimal places. The rounded probability of the factory producing exactly 5 defective items in a day, given an average of 4 faulty items, is 15.7%.

Part 3: Tips and tricks:

1. π The `POISSON.DIST` function is handy for rare events in large datasets.
2. π Ensure that the mean value you provide is non-negative. A negative mean will result in an error.
3. π Remember that the Poisson distribution assumes each event is independent of the others.
4. π For a visual representation, consider plotting the Poisson distribution using Excel’s charting tools.
1. π When using the `POISSON.DIST` function, ensure your dataset is large enough to provide a meaningful result.
2. π The `POISSON.DIST` function can be used to model random and independent events, such as the number of phone calls to a call center or the number of emails received in an hour.
3. π If you’re interested in the number of events over a different time frame or space, adjust the mean value accordingly.
4. π For more advanced statistical analysis, consider using other distribution functions in Excel or specialized statistical software.