Using the unscaled base rate
The mean argument belongs to the selected window. B2 alone ignores B3.
Scale an event-count model to its observation window
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Step-by-step guide · read-only ·
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Data & tools
Task requirements
Enter separate formulas in E2:E6. B2 is the assumed mean event count per base interval and B3 is the selected window divided by that base interval. E2 is their product. Under the stated constant-rate independent-event Poisson model, E3 is P(X=B4), E4 is P(X<=B4), E5 is P(B5<=X<=B6), and E6 is P(X>=B7). Keep the upper tail nonzero when it is very small; all probabilities are unrounded proportions.
Edit the event model
Apply one numeric value to the actual worksheet. Counts, proportions and interval boundaries keep their separate meanings. The complete model is validated before an edit replaces a valid input.
Applied value:
Follow the highlighted cells. Switch to Your turn to edit. Answer cells: E2, E3, E4, E5, E6. Browser calculations may differ from your Excel version.
Selection & formula search
Practice stays on this device. No worksheet data is uploaded.
Notes & examples
About this lesson
Convert a rate per base interval to a window mean, then report exact, cumulative, interval and upper-tail event probabilities.
THE QUICK ANSWER01
Convert a rate per base interval to a window mean, then report exact, cumulative, interval and upper-tail event probabilities.
E2
=$B$2*$B$3E3
=POISSON.DIST($B$4,$B$2*$B$3,FALSE)E4
=POISSON.DIST($B$4,$B$2*$B$3,TRUE)E5
=SUM(POISSON.DIST(SEQUENCE($B$6-$B$5+1,1,$B$5),$B$2*$B$3,FALSE))E6
=IF($B$7=0,1,GAMMA.DIST($B$2*$B$3,$B$7,1,TRUE))For the example data
E2 6E3 0.13385261753998337E4 0.2850565003166312E5 0.5889515171759268E6 0.7149434996833685
Enter each formula in its labeled answer cell. These report formulas perform different jobs; do not fill the first formula down.
How it works
Read the event before choosing a function
Enter separate formulas in E2:E6. B2 is the assumed mean event count per base interval and B3 is the selected window divided by that base interval. E2 is their product. Under the stated constant-rate independent-event Poisson model, E3 is P(X=B4), E4 is P(X<=B4), E5 is P(B5<=X<=B6), and E6 is P(X>=B7). Keep the upper tail nonzero when it is very small; all probabilities are unrounded proportions.
Keep the supplied model explicit
Use a numeric base mean from 0.01–30 and a numeric window ratio from 0.1–10, with their product at most 60. Whole exact/interval/threshold counts range from 0–100 and interval lower<=upper. No empirical event sequence is fitted; the mean and model assumptions are supplied. Requested positive outputs must remain representable in the supported numeric precision.
Retain full computed precision
Probability outputs are proportions, not percentages entered as whole numbers. Grading compares nonzero values relatively, so a rare positive event cannot pass as numeric zero. Full-precision copies keep the actual formula and result. The fitted or assumed model is not a guarantee of real outcomes.
Read the full step-by-step walkthrough
- Convert the interval before calculating probabilities
If the mean is three per base hour and the observation window is two hours, the model mean is six. Use a ratio of compatible durations, not an unlabelled clock time.
- Ask for one count or an inclusive cumulative count
POISSON.DIST uses the expected count for the complete window. FALSE selects exactly k; TRUE adds every whole count from zero through k.
- Sum the finite inclusive interval
SEQUENCE supplies every integer from a through b. SUM adds their probability masses. The single-point interval equals that point mass.
- Keep a rare upper tail measurable
For positive whole t, the Poisson upper tail equals GAMMA.DIST(window mean,t,1,TRUE). This incomplete-gamma identity avoids cancellation in 1-CDF for tiny tails. t=0 is certain and is handled explicitly.
- Separate assumptions from observed evidence
The task assumes a constant rate and independent event increments. Clustering, changing rates or capacity limits can invalidate this model; the worksheet does not establish those assumptions from the supplied number.
Things to watch
Subtracting nearly one from one
For very small upper tails, 1-CDF can round to zero. The gamma-CDF identity calculates the same event without that cancellation.
Confusing an expected count with certainty
The mean need not be a whole number and does not imply that the observed count will equal it.
About this example
Original source models checked with real browser formulas and independent combinatorial/series targets. Native execution remains separate.
Content version 1. Practice checks compare calculated results across different datasets; they do not certify every possible formula.