1. Investors use probabilities to decide among several potential investments and calculate potential returns, or losses. An investor has the possibility to invest $2 million in three different schemes. The first one has a 15% chance of returning $6 million profit, a 45% chance of returning $1 million and a 40% chance of losing $2 million. The second opportunity has a 30% chance of returning $2 million profit, a 30% chance of returning $1.5 million profit, and a 40% chance of losing $2 million. The third scheme has a 5% chance of returning $5 million profit, a 60% of no profit or loss, and a 35% chance of losing $2 million.
a. Construct a probability distribution function for each investment.
b. Find the expected value for each investment.
c. Calculate the standard deviation of investment 1.
d. Compare the standard deviations of each investment.
e. Which investment is the safest?
2. you are working as an assistant to the dean of institutional research at your university. The dean wants to survey members of the alumni association who obtained their baccalaureate degrees five years ago to learn what their starting salaries were in their first full-time job after receiving their degrees. A sample of 100 alumni is to be randomly selected from the list of 2,500 graduates in that class. If the dean's goal is to construct a 95% confidence interval estimate for the population mean starting salary, why is it not possible that you will be able to use Equation for this purpose? Explain.
X ± Za/2σ/√n