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 μ = 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 17?

(b)

What is the probability that the number of drivers will exceed 29?

(c)

What is the probability that the number of drivers will be between 17 and 29, inclusive?

What is the probability that the number of drivers will be strictly between 17 and 29?

(d)

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

Answer 1

Ans:

Use excel command Poisson(x,mean,true)

a)

P(x<=17)=Poisson(17,20,true)=0.297

b)

P(x>29)=1-P(x<=29)

  =1-Poisson(29,20,true)

=0.022

c)

P(17<=x<=29)=P(x<=29)-P(x<=16)

=Poisson(29,20,true)-Poisson(16,20,true)

=0.978-0.221

=0.757

P(17<x<29)=P(x<=28)-P(x<=17)

=Poisson(28,20,true)-Poisson(17,20,true)

=0.966-0.297

=0.669

d)

mean=20

standard deviation=sqrt(20)=4.5

P(20-2*4.5<=X<=20+2*4.5)

=P(11<=X<=29)

=P(X<=29)-P(X<=11)

=Poisson(29,20,true)-Poisson(11,20,true)

=0.978-0.021

=0.957