1. What is the value of , the parameter of exponential distribution? 2. What is

Question

1. What is the value of , the parameter of exponential distribution?

2. What is the standard deviation of time between successive arrivals?

3. What is the probability that the next drive thru arrival is between 2 to 4 minutes?

4. What is the probability that the next drive thru arrival is greater than 2 minutes given that it has been 1 minute since the last drive thru customer arrived?

5. What is the expected number of drive thru arrivals in 5 minutes?

6. What is the probability that there are exactly 2 drive thru arrivals in 5 minutes?

Let X the time between two successive arrivals at the drive thru window of the McDonald's on the North Atherton Street between 3 PM to 5 PM. Suppose X is exponentially distributed, and that the average time between successive arrivals at the drive thru window is 1.2 minute. Use this information and answer Question 1-6.

Explanation / Answer

1) =1/1.2

2) standard deviation of time =1/ =1.2

3) P(2<X<4) =e-2/1.2 -e-4/1.2 =0.1888-0.0357 =0.1532

4)P(X>2|X>1) =e-1/1.2 =0.4346

5)expected number of drive thru arrivals in 5 minutes =5/1.2=4.167

6)from poisson process

P(X=2) =e-(4.167)*(4.167)2/2! =0.1346

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