1. Section 6.3 The Poisson Probability Distribution
Obj: Use the Poisson distribution to find probability

2. Poisson Process
Definition: used to compute the probabilities of an event occurring within a specified interval. Criteria: 1. The probability of success is the same for any two intervals of equal length. 2. The number of successes in any interval is independent of the number of successes in any other interval. 3. The probability of 2 or more successes in a small subinterval is 0.

3. Example
A McDonald’s manager knows from prior experience that cars arrive at the drive- through at the constant rate of two cars per minute between the hours of 12:00 noon and 1:00 pm. The random variable x, the number of cars that arrive between 12:20 and 12:40, follows a Poisson process. This fits all three criteria.

4. Formulas
Poisson Probability Distribution Function x = number of successes λ = average t = time Mean of a Poisson Probability Distribution Function Standard Deviation of a Probability Distribution Function

5. McDonald’s Example
Find the probability that: 1. exactly 6 cars arrive between 12:00 and 12:05 Poissonpdf(μ, x) Poissonpdf(2∙5, 6) 2. fewer than 6 cars arrive between 12 and 12:05 Poissoncdf(μ, x) Poissoncdf(2∙5, 5) 3. at least 6 cars arrive between 12 and 12:05 1 – poissoncdf(10, 5)

6. Practice
The phone calls to a computer software help desk occur at the rate of 2.1 per minute between 3 pm and 4 pm. Compute the probability that the number of calls between 3:10 and 3:15 is:
exactly eight
fewer than eight
at least eight

7. Practice
A biologist performs an experiment in which Asian beetles are allowed to roam in an enclosed area of 1000 square feet. The area is divided into 200 subsections of 5 square feet each. Assuming that the beetles spread evenly throughout the enclosed area, how many beetles are expected to be within each subsection?
What is the standard deviation?
What is the probability of finding exactly 8 beetles in a particular subsection?
Would it be unusual to find more than 16 in one subsection?

8. Assignment
Section 6.3 page – 18