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 the total cost cannot be known with certainty ahead of time. Benzion Barlev of New York University proposed a model for the total cost of a long-term contract based on the normal distribution (Journal of Business Finance and Accounting, July 1995). Following Barlev’s idea, assume that the total cost of a particular contract is normally distributed with mean $850,000 and standard deviation $170,000. The revenue promised to the contractor is $1,100,000. The contract will lose money if the total cost exceeds revenue. Using the information about the contracts given above, what is the probability that the contract will lose money? Enter your answer to 4 decimal places. Refer to the context and numbers in the previous question. If the contractor has the opportunity to renegotiate the contract, what would revenue have to be in order to have a .95 probability of making a profit? Enter your answer as an integer (number of dollars).
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100,000. We can use the standard normal distribution to find this probability: z = (1.100,000 - 850,000) / 170,000 = 1.47 Using a standard normal distribution table or calculator, we can find that the probability of z being greater than 1.47 is 0.0708. Show more…
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