Question

# The number of people arriving for treatment at an emergency room can be modeled by a...

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?

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! = 0.735

(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

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