Problem 2 (20 points) Before negotiating a long-term construction contract, building contractors must carefully estimate the total cost of completing the project. The process is complicated by the fact that total cost cannot be known with certainty ahead of time. Benzion Barlev of New York University proposed a model for total cost of a long-term contract based on the normal distribution. For one particular construction contract, Barley assumed total cost, X to be normally distributed with mean $975,000 and standard deviation $150,000. The revenue, R, promised to the contractor is $1,250,000. a. The contract will be profitable if revenue exceeds total cost. What is the probability that the contract will be profitable for the contractor? Show your work. (5 points) b. What is the probability that the project will result in a loss for the contractor? Show your work. (4 points) c. What is the probability that the project will result in at least a $25,000 profit for the contractor? Show your work. (5 points) d. Suppose the contractor has the opportunity to renegotiate the contract. What value of R should the contractor strive for in order to have a .98 probability of making a profit? Show your work. (6 points)