A trucking firm has five trucks that each requires service at an average rate of

Question

A trucking firm has five trucks that each requires service at an average rate of once every 50 hours, according to an exponential distribution. The firm has a mechanic who needs five hours to complete the average job with exponential service times. What is the probability four or more of the trucks are in running order at a given time? (Note: For this question, if you assume that the workday for trucks and the mechanic are the same, then you can use the times as given without the need to consider that the mechanic doesn't work 24/7)

. a. Greater than 0.25 but less than or equal to 0.50

b. Greater than 0.50 but less than or equal to 0.75

c. Less than or equal to 0.25

d. Greater than 0.75

Explanation / Answer

Probability that the number of customers in the system is greater than k,Pn>k=(arrival rate/service rate)(k+1)

Service rate = 1/5 trucks/hour (5 hours taken to service 1 truck, hence, in one hour 1/5 trucks will be serviced)

Arrival Rate = 5/50 trucks/hour (5 trucks, with each truck coming every 50 hours, hence in one 1/50 truck will come, there are 5 trucks, hence 5*(1/50) trucks arrive per hour.

k=4 (given in the question)

Solving as per the above formula:

the probability four or more of the trucks are in running order at a given time = P =( (5/50)/(1/5)) (4+1) =0.3125

HEnce, Option a holds correct. a)Greater than 0.25 but less than or equal to 0.50

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