Question

Please explain step by step

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 u = 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? 0.011 (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?

Answer 1

x~possion($\mu$=20)

P(X = ?) - e-"* Hl"

Ans a:

P(X<11)

107 * 07- P(X <11) 0=

P(X <11) = Σ e-20 και 20 -= 0.021 ! =0

Ansb

P(X>26)

P(X>26)=1-P(x<=26)

26 P(X < 26) e-20 * 20" -= 0.922

P(X>26)=1-0.922

=0.078

Ans c:

26 P(11 < X < 26) => e-20 * 201 -= 0.913 I=11

#Probability of strictly between 11 and 26

= 25 -20 $ 20 P(11 < X < 26) = – = 0.866 . T=12

Ans d:

here mean =20

and std deviation =sqrt(20)=4.47

hence P(within 2 std deviation from mean )=P(20-2*4.47<X<20+2*4.47)=P(11.06 <X<28.94)=

Σ - 2020 /r1 T=12

=0.944