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 152 

(b) What is the probability that the number of drivers will exceed 297 

(c) What is the probability that the number of drivers will be between 15 and 29, inclusive? 

What is the probability that the number of drivers will be strictly between 15 and 297 

(d) What is the probability that the number of drivers will be within 2 standard deviations of the mean value?

Answer 1

a)

Mean/Expected number of events of interest: λ =                20

P(X<=15) =

=POISSON.DIST(15, 20, TRUE)

=0.157

B)

P(X>29)

= 1 - P(X<=28)

= 1 - 0.9657

=0.034

C)

P(15<=X<=29)

X	P(X)
15	0.0516
16	0.0646
17	0.0760
18	0.0844
19	0.0888
20	0.0888
21	0.0846
22	0.0769
23	0.0669
24	0.0557
25	0.0446
26	0.0343
27	0.0254
28	0.0181
29	0.0125

= 0.873

Not inclusive =

= 0.809

Please let me know in case of any doubt.

Thanks in advance!

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