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41 A construction company has taken up a project to build a high-rise office complex. The time required to complete a construction project is normally distributed with a mean of 80 weeks and a standard deviation of 10 weeks. A construction company must pay a penalty if the project is not finished by the due date in the contract. (a) If a construction company bidding on this contract puts in a due date of 80 weeks, what is the probability that they will have to pay a penalty? (b) If a construction company bidding on this contract wishes to be 90% sure of finishing by the due date, what due date (project week \#) should be negotiated? : 2-46 A local company that provides home repair services for appliances has two repairmen who make all of the home repairs. The company sends Repairman D on 70% of all jobs because the likelihood of him getting a second follow-up call within a week is only 0.08, whereas the probability of Repairman K getting a second follow-up call within a week is 0.20. If you recently had a repair job done at your home and it requires a second follow-up call, what is the probability that Repairman K did your initial repair work? 2-55 Nite Time Inn has a toll-free telephone number so that customers can call at any time to make a reservation. A typical call takes about 4 minutes to complete, and the time required follows an exponential distribution. Find the probability that a call takes (a) 3 minutes or less. (b) 4 minutes or less. (c) 5 minutes or less. (d) longer than 5 minutes