Problem 5. An investment fund manages investment portfolios of its clients. This fund follows a moderately conservative investment strategy, and observations from previous years show that the average yearly return on investment (ROI) of the fund is 16%. Suppose an investor wants to apply statistical analysis before deciding to invest in this fund. He assumes that the return of the fund has the normal distribution. (a) From past performance it is known that in 40% of cases the fund have the ROI at least 25%. Find the standard deviation of the fund's ROI. (b) Given the information from part (a), calculate the following investment performance mea- sures: (i) the probability for ROI to exceed 10%, (ii) the probability for the value of the portfolio to decrease by more than a half in a year, that is the probability for the ROI to be less than 50%. (c) Suppose there is another investment fund, which also seems to be promising from the investor's point of view. This fund has a more aggressive strategy, which results in the average ROI of 20%. The fund manager claims that the ROI of the fund exceeds 50% in 40% of cases. Compute the performance measure from part (b) for this fund. (d) Provide arguments for choosing the rst fund over the second one, and arguments for choosing the second fund over the rst one (If you think that one of these funds should not be chosen in any case, explain why you think so.)