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 a mean of 10, what is the probability that the number of drivers will be within 2 standard deviation of the mean value?

Answer 1

E(X) = 10 and V(X) = 10

p(μ − 2σ <= X <= μ+2σ) = p(10 − 2∗√10 <= X <= 10 + 2∗√10)

p( 3.67544468 <= X <= 16.32455532 ) = p( X <= 16 ) - p( X <= 3 )

p(X <= 16) = 0.9729583902

p(X <= 3) = 0.01033605068

p( 3.67544468 <= X <= 16.32455532 ) = 0.9729583902 - 0.01033605068 = 0.9626223393

Therefore, the probability that the number of drivers will be within 2 standard deviation of the mean value is 0.9626