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=20μ=20. What is the probability that the number of drivers is at least 16, i.e. P(X≥16)P(X≥16)? Use the Poisson probability table in the formula sheet.

Select one:

a. 0.779

b. 0.559

c. 0.441

d. 0.843

e. 0.221

Answer 1

Solution :

Given that ,

mean = $\mu$ =20

Using poison probability formula,

P(X = x) = (e-$\mu$ * $\mu$ x ) / x!

P(X > 16) = 1 - [P(X = 0)- P(X = 1)]-P(X = 2)- P(X = 3)- P(X = 4)- P(X = 5)- P(X = 6)- P(X = 7)- P(X = 8)- P(X = 9)- P(X = 10)- P(X = 11)- P(X = 12)- P(X = 13)- P(X = 14)- P(X = 15)- P(X = 16)

= 1 - (e-20 * 200) / 0! - (e-20 * 201) / 1!- (e-20 * 202) / 2!- (e-20 * 203) / 3!- (e-20 * 204) / 4!- (e-20 * 205) / 5!- (e- 20 * 206) / 6!- (e-20 * 207) / 7!- (e-20 * 208) / 8!- (e-20 * 209) / 9!- (e-20 * 2010) / 10!- (e-20 * 2011) / 11!- (e-20 * 2012) / 12!- (e-20 * 2013) / 13!- (e-20 * 2014) / 14!- (e-20 * 2015) / 15!- (e-20 * 2016) / 16!

=1-0.1565

Probability = 0.843

correct option is D