Suppose that the number of drivers who travel between a particular origin and de

Question

Suppose that the number of drivers who travel between a particular origin and destination during a designated time period has a Poisson distribution with parameter = 20 (suggested in the article "Dynamic Ride Sharing: Theory and Practice"). (Round your answer to three decimal places.) (a) What is the probability that the number of drivers will be at most 11? (b) What is the probability that the number of drivers will exceed 26? (c) What is the probability that the number of drivers will be between 11 and 26, inclusive? What is the probability that the number of drivers will be strictly between 11 and 26? (d) What is the probability that the number of drivers will be within 2 standard deviations of the mean value? You may need to use the appropriate table ithe ARpendix of Tables to answer this question.

Explanation / Answer

Poisson parameter = 20

a) if x is number of drivers who travel between particular origin and destination

Pr(x 11) = POISSON (x 11; 20) = 0.0214

(b) Pr(x > 26) = POISSON (x > 26 ; 20) = 1 - POISSON (x 26; 20) = 1 - 0.9221 =0.0779

(c) Pr(11 x 26) = POISSON (x 26) - POISSON (x < 11) = 0.9221 - 0.0108 = 0.9113

Pr(11 < x < 26) = POISSOn (x < 26) - POISSON (x 11) = 0.8878 - 0.0214 = 0.8664

(d) Here standard deviation std(x) = sqrt (20) = 4.4721

two standard deviation away values = (20 -2 * 4.471 + 20 + 2 * 4.471) = (11.0557, 28.9443)

so values within 2 standard deviation are

Pr(11.0557 < x < 28.9443) = Pr(12 x 28) = POISSOn (x 28; 20) - POISSON (x < 12 ; 20) = 0.9657 - 0.0214 = 0.9443

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