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1.It is known that 15% of all homeowners pay a monthly mortgage of more than $2500 and that the standard deviation of the monthly mortgage payments of all homeowners is $350. Suppose that the monthly mortgage payments of all homeowners have a normal distribution. What is the mean monthly mortgage paid by all homeowners? 2.Two companies, A and B, drill wells in a rural area. Company A charges a flat fee of $3500 to drill a well regardless of its depth. Company B charges $1000 plus $12 per foot to drill a well. The depths of wells drilled in this area have a normal distribution with a mean of 250 feet and a standard deviation of 40 feet.What is the probability that Company B would charge more than Company A to drill a well? 3.An insurance company looks at the records for millions of homeowners and sees that the mean loss from fire in a year is $300 per person and the standard deviation of the loss is $400.What are the mean and standard deviation of the average loss for 10 policies? (losses on separate policies are independent) 4.Call a household prosperous if its income exceeds $100,000. Call the household educated if the household completed college. Select an American household at random, and let A be the event that the selected household is prosperous and B the event that it is educated. According to the Current Population Survey, P(A)=0.138, P(B)=0.261 and the probability that a household is both prosperous and educated is P(A and B)=0.082.What is the probability that a household is prosperous given that it is educated? 5.The College Board finds that the distribution of students' SAT scores depends on the level of education their parents have. Children of parents who did not finish high school have SAT math scores X with mean 445 and standard deviation 106. Scores Y of children of parents with graduate degrees have mean 566 and standard deviation of 109. Perhaps we should standardize to a common scale for equity. Find positive numbers a, b, c and d such that a+bX and c+dY both have mean 500 and standard deviation 100. Assume b and d are positive.

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