XLSTAT: Probability Calculator in Excel

 

Background

A probability distribution is a mathematical function (or measure) that links random events to their likelihood. It helps model uncertainty in scenarios such as:

• Rolling a die (e.g., probability of getting a 2)

• Simultaneous arrival of customers

• Drawing a King from a deck

Randomness reflects limited knowledge. While die rolls could theoretically be predicted with perfect data, complexity makes it practical to model outcomes probabilistically.

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Example: Email arrivals modeled by a Poisson distribution with average rate λ = 5

We want to calculate:

1. P(receive 10 emails)

2. P(receive between 3 and 6 emails)

3. Number of emails where P(X ≤ x) = 0.8 (80th percentile)

4. Visualize the probability mass function (PMF)

These can be computed using statistical software or functions like:

• POISSON.DIST(x, λ, FALSE) in Excel for exact values

• POISSON.DIST(x, λ, TRUE) for cumulative values

• A bar chart to display the PMF (probability for x = 0 to, say, 15)

 

Setting Up

• Open XLSTAT.

• Click on the Mathematical tools menu and select the Probability Calculator feature.

 

• The  Probability Calculator dialog box appears.

• In the dialog box:

  • Left panel:

    • Select the Poisson distribution from the dropdown.

    • Enter the parameter λ = 5.

    • Choose to compute the density, CDF, or inverse CDF, depending on the goal.

  • Middle panel:

    • Specify the output location.

    • Choose to display the computed probability within the interface.

  • Right panel:

    • View the distribution function (PMF or CDF) graphically.

• Enter 5 in the lambda field, representing the average daily email count. Lambda is the event rate or rate parameter of the Poisson distribution.

 

What is the probability to receive 10 emails in a day?

 

 

What is the probability to receive between 3 and 6 emails in a day?

Which is the number of received emails in a day such as the probability to receive this amount is 0.8?