Two more statistic questions?

1. Cystic fibrosis is a lung disorder that often results in death. It is inherited but can be inherited only if both parents are carriers of an abnormal gene. In 1989, the CF gene that is abnormal in carriers of cystic fibrosis was identified. The probability that a randomly chosen person of European ancestry carries an abnormal CF gene is 1/25. The CF20m test detects most but not all harmful mutations of the CF gene. The test is positive for 90% of people who are carriers. It is never positive for people who are not carriers.
- Jason tests positive. What is the probability that he is a carrier?
- 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.


2. 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)
- What are the mean and standard deviation of the average loss for 12 policies? (Losses on separate policies are independent)