T T05-02 Poisson Distribution Purpose Allows the analyst to analyze a Poisson Distribution. Probability Scenario's, Expected Value, Variance and Standard Deviation of the Poisson Distribution are calculated. Inputs – expected number of successes Probability Scenario Outputs Poisson Probability Distribution Cumulative Probability Distribution Probability Scenario Solution Expected Value, Variance & Standard Deviation Graph of Poisson Distribution Limitations 50 successes or less

T An Example The number of people who arrive at a checkout counter at a local supermarket during a specified period of time approximates a Poisson distribution. If the expected number of people who arrive at a checkout counter are 2 people per minute, What is the probability that at any given minute the number of arrivals will be. At least 3. 1 or less. Between 4 and 6 (non-inclusive)

T p ( x ) = Probability of x given =Expected (mean) number ‘successes’ e = (base of natural logs) x =Number of ‘successes’ in per unit MeanStandard Deviation Poisson Probability Distribution px x () ! xe-

T Expected Successes are entered here.

T The Poisson Distribution P(X) and CP(X) are automatically calculated for successes. Also, the Expected Value, Variance and Standard Deviation are automatically calculated.

T If a valid value for X is entered (automatically validated), the probability scenario can be quickly answered by inputting the information in the light green cells. The answer to the scenario is automatically calculated.

T The Discrete Poisson Probability Distribution is shown as a bar graph.