Suppose that the number of drivers who travel between a Problem 81E Chapter 3

Probability and Statistics for Engineering and the Sciences | 9th Edition

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Problem 81E

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,” J. of Transp. Engr., 1997: 308–312). What is the probability that the number of drivers will a.? e at most 10? b.?? xceed 20? c.? e between 10 and 20, inclusive? Be strictly between 10 and 20? d.? ?Be within 2 standard deviations of the mean value?

Step-by-Step Solution:

Solution Step 1 : Here X is the number of drivers who traveled between a particular origin and destination during a designated time period follows a Poisson distribution with parameter =20 . we have to find probabilities corresponds to different X values. Step 2 : a) We have to find the probability that the number of drivers will be at most 10. It is given that the random variable X follows poisson distribution with parameter (mean) = 20. The probability mass function of poisson distribution is x e P(x) = x! , x= 0,1,2,3,... So the probability that the number of drivers will be at most 10 is 10 e x P(X10)= x! x=0 10 e20 20x = x! x=0 = P(x=0)+p(x=1)+p(x=2)+...+P(x=10) = 0.00+0.000+0.00+0.00+0.00001+.00005+0.00018+...+.00581 = 0.0108 We can find this probability in excel also by using the function (POISSON(X,MEAN,CUMULATIVE= FALSE),then SUM(CELL NUMBERS) ).

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ISBN: 9780321629111

The full step-by-step solution to problem: 81E from chapter: 3 was answered by , our top Statistics solution expert on 05/06/17, 06:21PM. The answer to “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,” J. of Transp. Engr., 1997: 308–312). What is the probability that the number of drivers will a.? e at most 10? b.?? xceed 20? c.? e between 10 and 20, inclusive? Be strictly between 10 and 20? d.? ?Be within 2 standard deviations of the mean value?” is broken down into a number of easy to follow steps, and 84 words. This full solution covers the following key subjects: Drivers, period, destination, deviations, distribution. This expansive textbook survival guide covers 18 chapters, and 1582 solutions. This textbook survival guide was created for the textbook: Probability and Statistics for Engineering and the Sciences, edition: 9. Probability and Statistics for Engineering and the Sciences was written by and is associated to the ISBN: 9780321629111. Since the solution to 81E from 3 chapter was answered, more than 1158 students have viewed the full step-by-step answer.

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