Jenn Bard, who lives in San Francisco Bay area, commutes by car from home to work. She has found out that it takes her an average of 28 minutes for…

Jenn Bard, who lives in San Francisco Bay area, commutes by car from home to work. She has found out that it takes her an average of 28 minutes for this commute in the morning. However, due to the variability in the traffic situation every morning, the standard deviation of these commutes is 5 minutes. Suppose the population of her morning commute times has a normal distribution with a mean of 28 minutes and a standard deviation of 5 minutes. Jenn has to be at work by 8:30AM every morning. By what time must she leave home in the morning so that she is late for work at most 1% of the time?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?Jason knows that he is a carrier of CF. His wife, Julianne, has a brother with CF, which means the probability is 2/3 that she is a carrier. If Julianne is a carrier, each child she has with Jason has probability of 1/4 of having CF. If she is not a carrier, her children cannot have the disease. Jason and Julianne have one child, who does not have CF. This information reduces the probability that Julianne is a carrier. Use Bayes’ rule to find the conditional probability that Julianne is a carrier, given that she and Jason have one child who does not have CF.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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