1-The Capital Asset Pricing Model (CAPM) is a financial model that assumes returns on a portfolio are normally distributed. Suppose a portfolio has an average annual return of 14.7% (i.e. an average gain of 14.7%) with a standard deviation of 33%. A return of 0% means the value of the portfolio doesn't change, a negative return means that the portfolio loses money, and a positive return means that the portfolio gains money. (please round answers to within one hundredth of a percent) (a) What percent of years does this portfolio lose money, i.e. have a return less than 0%?

(b) What is the cutoff for the highest 15% of annual returns with this portfolio?

2-The physical fitness of an athlete is often measured by how much oxygen the athlete takes in (which is recorded in milliliters per kilogram, ml/kg). The mean maximum oxygen uptake for elite athletes has been found to be 67 with a standard deviation of 8. Assume that the distribution is approximately normal.

Hint: Find the probability a normal random variable is in the right tail or the left tail.

Find the probability that an elite athlete has a maximum oxygen uptake of at least 87.8 ml/kg.

Find the probability that an elite athlete has a maximum oxygen uptake of at most 59 ml/kg

3-The average American man consumes 9.9 grams of sodium each day. Suppose that the sodium consumption of American men is normally distributed with a standard deviation of 0.9 grams. Suppose an American man is randomly chosen. Let X = the amount of sodium consumed. Round all numeric answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N( , )

b. Find the probability that this American man consumes between 10 and 11.7 grams of sodium per day.

c. The middle 20% of American men consume between what two weights of sodium? Low: High: