Question

The number of people arriving for treatment at an emergency room can be modeled by a Poisson process with a rate parameter of five per hour. By using Poisson Distributions. Find:

(i) What is the probability that exactly four arrivals occur during a particular hour?

(ii) What is the probability that at least four people arrive during a particular hour?

(iii) What is the probability that at least one person arrive during a particular minute?

(iv) How many people do you expect to arrive during a 50- min period?

Answer 1

i)

this is Poisson distribution with parameter λ=5

  probability that exactly four arrivals occur during a particular hour:

P(X=4)=

{e-5*54/4!} =

0.1755

(Note:

if using ti-84 use commannd :poissonpdf(5,4)

if using excel use commannd :poisson(4,5,false)

)

ii)

probability that at least four people arrive during a particular hour:

P(X>=4)=1-P(X<=3)=

1-∑x=0x e-λ*λx/x! =

0.7350

(Note:

if using ti-84 use command :1-poissoncdf(5,3)

if using excel use commannd :1-poisson(3,5,true)

)

iii) expected number in 1 minute =5/60=1/12

probability that at least one person arrive during a particular minute:

P(X>=1) =1-P(X=0) =1-e-1/12 =0.0800

iv)

expected number of arrivals in 50 min period =50*5/60= 4.167