Assumptions of the Poisson Distribution 1 The probability is proportional to

# Assumptions of the poisson distribution 1 the

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Assumptions of the Poisson Distribution (1) The probability is proportional to the length of the interval. (2) The intervals are independent. Also known as the "Law of Improbable Events" Limited form of Binomial (very small S , very large n) 203
Poisson Probability Distribution The Poisson probability distribution is characterized by the number of times an event happens during some interval or continuum. Examples include: • The number of misspelled words per page in a newspaper. • The number of calls per hour received by Dyson Vacuum Cleaner Company. • The number of vehicles sold per day at Hyatt Buick GMC in Durham, North Carolina. • The number of goals scored in a college soccer game. 203 Poisson Probability Distribution The Poisson distribution can be described mathematically using the formula: 204
Poisson Probability Distribution z The mean number of successes ȝ can be determined in binomial situations by n S , where n is the number of trials and S is the probability of a success. z The variance of the Poisson distribution is also equal to n S . 204 Assume baggage is rarely lost by Northwest Airlines. Suppose a random sample of 1,000 flights shows a total of 300 bags were lost. Thus, the arithmetic mean number of lost bags per flight is 0.3 (300/1,000). If the number of lost bags per flight follows a Poisson distribution with μ = 0.3, find the probability of not losing any bags in a specific flight. What is the Interval? A FLIGHT NOTE: μ calculated by observation, NOT n S Poisson Probability Distribution - Example 204
Poisson Probability Distribution - Table Recall from the previous illustration that the number of lost bags follows a Poisson distribution with a mean of 0.3. Use Appendix B.5 to find the probability that no bags will be lost on a particular flight. What is the probability exactly one bag will be lost on a particular flight? 205 Example from text - variation (comparing Poisson vs. Binomial): we'll just do P(0), not 1 - P(0) z Probability of hurricane hitting in a year is 0.05 z What is the probability of 0 in 30 years? z Poisson: z Binomial: 206 S P n # ! ) ( x e x P u x 0 P x n x x n C x P 0 0 ) 1 ( ) ( S S 22313 . 0 ! 0 5 . 1 ) 0 ( 5 . 1 5 . 1 0 0 0 e e P 5 . 1 05 . 0 30 x # P 21464 . 0 95 . 0 ) 05 . 1 ( 30 30 0 n P ) 1 ( ) 0 ( S 0
More About the Poisson Probability Distribution •The Poisson probability distribution is always positively skewed and the random variable has no specific upper limit. •The Poisson distribution for the lost bags illustration, where μ=0.3, is highly skewed. As μ becomes larger, the Poisson distribution becomes more symmetrical. 207 MGMT 2340 Section W01 Business Statistics I Instructor: E. Mark Leany contact via Blackboard online.uen.org alternately: [email protected]

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• Spring '11
• Leany
• Poisson Distribution, Probability distribution, Probability theory, Binomial distribution, Discrete probability distribution