3. QUEUING THEORY-POISSON Complete the problem below: Customers arrive at the lo

Question

3. QUEUING THEORY-POISSON Complete the problem below: Customers arrive at the local Kline's Ice Cream Parlor at an average rate of 16 per hour. Follow the Poisson distribution to answer the following questions: 1. What is the probability that two customers will arrive during the next 15 minutes? 2 What is the probability that four customers will arrive during the next 15 minutes? 3. What is the probability that six customers will arrive during the next 30 minutes? 4 What is the probability that six customers will arrive during the next 45 minutes?

Explanation / Answer

lambda=16 per hour = 4(15 min) = 8(30 min) = 12(45 min)

P(x)=e(-lambda)*lambda^x/x!

1. For 2 customer we have to calculate P(2),

With x = 2, using above formula we have

P(2)= e^(-4)(4^2)/2! = 0.1465

2. Similar for 4 customer in next 15 min,

P(4)= e^(-4)(4^4)/4! = 0.1954

3. For this we have lambda = 8;

Using same formula as above,

P(6) = e^(-8)(8^6)/6! = 0.1221

4. For six customer in next 45 min, we have lambda = 12.

P(6)=e^(-12)*12^6/6!

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