1) The following table summarizes the average annual return and the standard deviation of returns for several types of securities over the past 75 years. Investment Small-Cap Common Stock Large Cap Common Stock Long-Term Bonds Treasury Bills Mean Returns .170 .110 .080 .035 Standard Deviation .350 .230 .040 .031 Assume annual returns in each case are approximately normal distributed around the mean rate. Using this historical information as the basis for your calculation, what is the probability of loss over the next year if you put all of your money into? a) Small cap stocks b) Large cap stock c) Long term bonds d) Treasury bills 2) Refer to exercise 1 a) Suppose you invest $10,000 in large cap stock. Using the historical performance data showing in the table, how likely is tit that you will end up making more than $4,400 for the year? b) Suppose you invest $10,000 in long term bonds. How likely is it that you will end up losing at least $200 for the year? c) Suppose you invested 2000 in small cap stock. Determine the probability that the investment will produce a return of less than $500. 3) Your firm produced precision engine parts that must conform to fairly rigid diameter specification, diameters follow a normal distribution with a mean of 125 mm and a standard deviation of 4mm. what percentage of diameters will be a) between 120 and 130mm b) between 131 and 133mm c) less than 136mm d) more than 132mm e) less than 116mm