SOLUTION: 3) Suppose the time it takes for customer representatives to diagnose and fix computer problems is uniformly distributed from 10 to 120 minutes. a. What is the probability that a

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Question 1180931: 3) Suppose the time it takes for customer representatives to diagnose and fix computer problems is
uniformly distributed from 10 to 120 minutes.
a. What is the probability that a problem is diagnosed and fixed within 30 minutes?
b. What is the probability that it takes longer than 90 minutes to diagnose and fix a computer problem?
c. What is the average time for customer representatives to diagnose and fix computer problems?

Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52835)   (Show Source): You can put this solution on YOUR website!
.

(a)  The events are within the 30 minutes time interval of the total  110 = 120-10 minutes.


     THEREFORE,  P =  = 0.2727... = 0.2727  (rounded) = 27.27%.    ANSWER



(b)  This time the events are within of 30 minutes time interval  (30 = 120-90) 
 of the total  110 = 120-10 minutes, so AGAIN


                 P =  =  = 0.2727... = 0.2727  (rounded)  = 27.27%.    ANSWER



(c)  Average time  is   =  = 65 minutes.    ANSWER


Solved.   //     All questions are answered.



Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


For part a, I will disagree with tutor @ikleyn. Since the distribution is uniform between 10 and 120 minutes, I interpret that to mean the probability of having the diagnosis complete in less than 10 minutes is 0.

Therefore the diagnosis times that are less than 30 minutes are between 10 and 30 minutes instead of between 0 and 30 minutes. That makes the probability in this case 20/110 = 2/11.
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