Advanced Math Topics 6 7 The Poisson Probability

Advanced Math Topics 6. 7 The Poisson Probability Formula

The Poisson formula allows us to find the probability of an event happening over a period of time(or in a region) if we know the expected amount (mean) over the period of time. Where μ is the average number of successes occurring in a given time and x = 0, 1, 2, 3, …. e-μ • μx p(x successes) = x! The conditions that must be met are… 1) Each “success” is independent of the others 2) The probability of success in an interval(or region) is very small http: //en. wikipedia. org/wiki/Poisson_distribution

-μ • μx e p(x successes) = x! The mean number of wrong number calls received by a telephone operator during lunch hour is 4. Find the probability that… a) The operator receives exactly 2 wrong number calls during the lunch hour. -4 • 42 e p(2 successes) = =. 01832 • 16 =. 1465 2! 2 = 14. 65% You may use your calculator to find e-4 or Table XII in the appendix. b) The operator receives at most 2 wrong number calls during the lunch hour. p(at most 2 successes) = p(0) + p(1) + p(2) -4 • 40 e =. 01832 p(0) = 0! Add them up… -4 1 p(1) = e • 4 =. 07328 1!. 2381 = 23. 81% p(2) =. 1465

From the HW P. 334 1) A newspaper stand averages 5 customers per minute during the rush hour. Find the probability that… a) At most 2 customers will arrive. 12. 47% b) At least 2 customers will arrive. 95. 96% c) Exactly 2 customers will arrive. 8. 43%

HW P. 334 #1 -8 Just a reminder of what’s allowed in the bins: EMPTY plastic bottles, aluminum cans, and paper. Whats NOT allowed: wrappers, gum, Ziploc baggies, half-empty beverages. If these items are in the bins, then the whole bin gets dumped into the trash. Last week, I spent the first 5 minutes of each class demonstrating what goes in each receptacle. Since this small demonstration, my students have been very good about proper placement of waste items in my classroom.