Round to 4 significant figures In a waiting line situation, customer arrivals oc

Question

Round to 4 significant figures In a waiting line situation, customer arrivals occur around the clock at a rate of 6 per day, and the service occurs at one every 3 hours. A) What is the arrival rate in hours? B) What is the service rate in hours? C) What is the probability that 2 orders arrive in 6 hours? First, What is the parameter Lambda here? Next, what is the probability asked above? D) Find probability that at least one order arrives in 3 hours First, What is the parameter Lambda here? Next, what is the probability asked above? E) Find probability that 3 orders are serviced in 6 hours. First, What is the parameter Lambda here? Next, what is the probability asked above?

Explanation / Answer

A)
Arrival rate = 6 per day = 6/24 = 1/4 per hour

B)
Service rate = 1/3 per hour

C)
lambda = 1/4*6 = 3/2
P(X=2) = e^(-3/2)*(3/2)^2 / 2! = 0.2510

D)
lambda = 1/4*3 = 3/4
P(X>=1) = 1 - P(X=0)
P(X=0) = e^(-3/4)*(3/4)^0 / 0! = 0.4724

P(X>=1) = 1 - P(X=0) = 1 - 0.4724 = 0.5276

E)
lambda = 6/3 = 2
P(X=3) = e^(-2)*(2)^3 / 3! = 0.1804

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