Model for long-term construction cost. before negotiating a long term

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Model for long-term construction cost. Before negotiating a long term contract, building contractors must carefully estimate the total cost of completing the project. Benzion Barlev of New York University proposed a model for total cost of a long-term contract based on the normal distribution (Journal of Business Finance and Accounting, July 1995). For one particular construction contract, Barlev assumed total cost, x, to be normally distributed with mean $850,000 and standard deviation $170,000. The revenue, R, promised to the contractor is $1,000,000.

a. The contract will be profitable if revenue exceeds total cost. What is the probability that the contract will be profitable for the contractor?

b. What is the probability that the project will result in a loss for the contractor?

c. Suppose the contractor has the opportunity to renegotiate the contract. What value of R should the contractor strive for in order to have a .99 probability of making a profit?