A dentist sees on average 7.0 patients a day.
· what is the probability that she will see four patients?
· what is the probability that she will see less than 3 patients?
· Average (the statistics symbol for average is μ) μ = 7
I like using StatTrek to look up Statistical Formulas and Definitions.
Here is the page that explains the Poisson Distribution formula http://stattrek.com/probability-distributions/poisson.aspx
Poisson Formula. Suppose we conduct a Poisson experiment, in which the average number of successes within a given region is μ. Then, the Poisson probability is:
P(x; μ) = (e-μ) (μx) / x!
where x is the actual number of successes that result from the experiment, and e is approximately equal to 2.71828.
Our example we can plug in these numbers
P = Probability
X = 4
μ = 7
e = 2.71828
· Our Poisson Formula – when we plug in the numbers looks like this:
· P(x; 7) = (2.718828-7)(74) / 4 which is approx. .09
· There is a calculator at the bottom of the page so you can check your calculation
To test to see if your calculations are correct, basically you want the probabilities to equal 1 if your looking for 4 then:
When you add the: Less than 4 + Equal to 4 + Greater than 4 should add up to 1 or 1.00 or 100%
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Now if we want to know the probability that she will see less than 3 patients?
That is actually the Probability of 0 patients + 1 patient + 2 patients
P(x; < 3) = (2.718828-3)(73) / 3