There is an average of 5 minutes (distributed exponentially) between calls at th

Question

There is an average of 5 minutes (distributed exponentially) between calls at the Information Technology Help Desk of a large organization during normal office hours. Use appropriate Excel functions to solve the following questions:

(1) (To three decimal places) Compute the probability of it taking less than 3 minutes to receive a phone call.

(2) (To three decimal places) Compute the probability of taking at least 7 minutes to receive a call.

(3) (To three decimal places) Compute the probability of it taking between 4 and 8 minutes to receive a call.

(4) (To three decimal places) The current call at a help desk is going to take 4 minutes to complete. There is only this one phone line at the help desk. Compute the probability the they will be able to complete the call without the next caller having to wait on hold.

(5) (To three decimal places) Compute the probability that it will take at least 6 minutes until the next phone call.

The time period required to pass through security screening at the airport can be annoying to travelers. The mean wait time during peak periods at a particular International Airport is 13.6 minutes. Assume the time to pass through security screening follows an exponential distribution.

(6) (To three decimal places) Compute the probability it will take less than 7 minutes to pass through security screening during a peak period.

(7) (To three decimal places) Compute the probability it will take more than 18 minutes to pass through security screening during a peak period.

(8) (To three decimal places) Compute the probability it will take between 12 and 19 minutes to pass through security screening during a peak period.

(9) (To three decimal places) It is 8:00am (a peak period) and you just entered the security line. To catch your plane you must be at the gate within 25 minutes. If it takes 15 minutes from the time you clear security until you reach your gate, compute the probability you will miss your flight.

(10) (To three decimal places) You watched the last traveler to go through security took her 5 minutes to pass through security screening (it is a peak hour). Compute the probability that if you entered the security screening right now that you would be able to pass through in under 11 minutes?

Explanation / Answer

1) here lambda =1/5

hence P(X<3) =expondist(3,1/5,true)=0.451

2) =1-expondist(7,1/5,true)=0.247

3)P(4<X<8) =expondist(8,1/5,true)-expondist(4,1/5,true)=0.247

4) =1-expondist(4,1/5,true)=0.449

5)=1-expondist(6,1/5,true)=0.301

lambda =1/13.6

6) probability it will take less than 7 minutes to pass =expondist(7,1/13.6,true) =0.402

7)probability it will take more than 18 minutes to pass =1-expondist(18,1/13.6,true) =0.247

8) probability it will take between 12 and 19 minutes to pass through security screening during a peak period.

=expondist(19,1/13.6,true)-expondist(12,1/13.6,true)=0.166

9)=1-expondist(25,1/15,true) =0.189

10)expondist(11,1/5,true) =0.889

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