6.12 A contractor must pay a$40,000 penalty if construction of an expensive home

Question

6.12 A contractor must pay a$40,000 penalty if construction of an expensive home requires morethan 16 weeks. He will receive a bonus of $10,000 if the home iscompleted within 8 weeks. Based on experience with this type ofproject, the contractor feels there is a 0.2 chance the home willrequire more than 16 weeks for completion, and there is a 0.3chance it will be finished within 8 weeks. If the price of the homeis $350,000 before any penalty or bonus adjustment, how much canthe buyer expect to pay for her new home when it is completed?

Explanation / Answer

collect information: - 40.000 if x>16 10.000 if x < 8 p(x>16)=0.2 p(x<8) = 0.3 p(8 < x < 16) =0.5 Calculate the expected loss/win : E(X) = 0.2*-40.000 +0.3*10.000 = -8000 + 3000 = -5000 Expected price = -5000 + 350.000 = 345.000

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