FULL SCREEN PRINTER VERSIO A university police department receives an average of
ID: 3238356 • Letter: F
Question
FULL SCREEN PRINTER VERSIO A university police department receives an average of 3.9 reports per week of lost student ID cards. Round your answers to four decimal places. a. Find the probability that at most 1 such report will be received during a given week police department. Use the Poisson probability distribution formula. by this Pl at most 1) b. Using the Poisson probabilities table, find the probability that during a given week the number of such reports received by this police department is i. 3 to 6 3 to 6) ii. at least at least 6) at most 3) All Rights Reserved Division of MacBook AirExplanation / Answer
= 3.9, P(x) = (e^-)(^x) / x!
(a) P(x 1) = P(0) + P(1) = (e^-3.9)(3.9^0) / 0! + (e^-3.9)(3.9^1) / 1! = 0.0992
(b) (i) P(3 x 6) = P(3) + P(4) + P(5) + P(6)
= (e^-3.9)(3.9^3) / 3! + (e^-3.9)(3.9^4) / 4! + (e^-3.9)(3.9^5) / 5! + (e^-3.9)(3.9^6) / 6! = 0.6464
(ii) P(x 6) = 1 - P(x < 6) = 1 - [P(0) + P(1) + P(2) + P(3) + P(4) + P(5)]
= 1 - [(e^-3.9)(3.9^0) / 0! + (e^-3.9)(3.9^1) / 1! + (e^-3.9)(3.9^2) / 2! + (e^-3.9)(3.9^3) / 3! + (e^-3.9)(3.9^4) / 4! + (e^-3.9)(3.9^5) / 5!] = 0.1994
(iii) P(x 3) = P(0) + P(1) + P(2) + P(3)
= (e^-3.9)(3.9^0) / 0! + (e^-3.9)(3.9^1) / 1! + (e^-3.9)(3.9^2) / 2! + (e^-3.9)(3.9^3) = 0.4532.
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