The manager of a construction job needs to figure prices carefully before submitting a

Chapter 6, Problem 6.45

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The manager of a construction job needs to figure prices carefully before submitting a bid. He also needs to account for uncertainty (variability) in the amounts of products he might need. To oversimplify the real situation, suppose that a project manager treats the amount of sand, in yards, needed for a construction project as a random variable Y1, which is normally distributed with mean 10 yards and standard deviation .5 yard. The amount of cement mix needed, in hundreds of pounds, is a random variable Y2, which is normally distributed with mean 4 and standard deviation .2. The sand costs $7 per yard, and the cement mix costs $3 per hundred pounds. Adding $100 for other costs, he computes his total cost to be U = 100 + 7Y1 + 3Y2. If Y1 and Y2 are independent, how much should the manager bid to ensure that the true costs will exceed the amount bid with a probability of only .01? Is the independence assumption reasonable here?