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gayaneshka [121]
2 years ago
9

The number of people arriving for treatment at an emergency room can be modeled by aPoisson process with a rate parameter of 5/h

r.(a) What is the probability thatexactly fourarrivals occur during a particular hour?(b) What is the probability thatat least threepeople arrive during a particular hour?(c) How many people do you expect to arrive during a45-minuteperiod?
Mathematics
1 answer:
saveliy_v [14]2 years ago
8 0

Answer:

(a) The probability of having exactly four arrivals during a particular hour is 0.1754.

(b) The probability that at least 3 people arriving during a particular hour is 0.7350.

(c) The expected arrivals in a 45 minute period (0.75 hours) is 3.75 arrivals.

Step-by-step explanation:

(a) If the arrivals can be modeled by a Poisson process, with λ = 5/hr, the probability of having exactly four arrivals during a particular hour is:

P(X=4)=\frac{\lambda^{X}*e^{-\lambda}  }{X!} =\frac{5^{4}*e^{-5}  }{4!}=\frac{625*0.006737947}{24} =\frac{4.211}{24}=0.1754

The probability of having exactly four arrivals during a particular hour is 0.1754.

(b) The probability that at least 3 people arriving during a particular hour can be written as

P(X>3)=1-P(X\leq3)=1- (P(0)+P(1)+P(2)+P(3))

Using

P(X)=\frac{\lambda^{X}*e^{-\lambda}  }{X!}

We get

P(X>3)=1-P(X\leq3)=1- (P(0)+P(1)+P(2)+P(3))\\P(X>3)=1-(0.0067+ 0.0337+ 0.0842 + 0.1404 )\\P(X>3)=1-0.2650=0.7350\\

The probability that at least 3 people arriving during a particular hour is 0.7350.

(c) The expected arrivals in a 45 minute period (0.75 hours) is

EV=\lambda*t=5*0.75=3.75

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