The Poisson Probability Calculator can calculate the probability of an event occurring in a given time interval.  Before using the calculator, you must know the average number of times the event occurs in the time interval.  The symbol for this average is $ \lambda $, the greek letter lambda.  You also need to know the desired number of times the event is to occur, symbolized by x.

The Poisson Probability Calculator can calculate the probability of an event occurring in a given time interval. 

If you’d like to construct a complete probability distribution based on a value for $ \lambda $ and x, then go ahead and take a look at the Poisson Distribution Calculator.  It will calculate all the poisson probabilities from 0 to x.

Poisson Probability Calculator

Answer:

$ P(8) $ Probability of exactly 8 occurrences: 0.10989734608285


Solution:

$P(8)$ Probability of exactly 8 occurrences

If using a calculator, you can enter $ \lambda = 6.2 $ and $ x = 8 $ into a poisson probability distribution function (PDF). If doing this by hand, apply the poisson probability formula: $$ P(x) = \frac{{e^{-\lambda}} \cdot {\lambda^x}}{x!} $$ where $x$ is the number of occurrences, $\lambda$ is the mean number of occurrences, and $e$ is the constant 2.718. Substituting in values for this problem, $ x = 8 $ and $ \lambda = 6.2 $, we have $$ P(8) = \frac{{e^{-6.2}} \cdot {6.2^8}}{8!} $$ Evaluating the expression, we have $$ P(8) = 0.10989734608285 $$

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