1. You are examining the record of an investment newsletter writer who claims a 70 percent success rate in making investment recommendations that are profitable over one-year time horizon. You are independent and the newsletter writer's skill is as claimed, what is the mendations. Four of those recommendations were profitable. If all the recommendations are independent and the newsletter writer‘s skills is as claimed, what is the probability of observing four or fewer profitable recommendations out of seven in total?
2. State the approximate probability that a normal random variable will fall within the following intervals:
A. Mean plus or minus one standard deviation.
B. Mean plus or minus two standard deviations.
C. Mean plus or minus three standard deviations.
3. Find the area under the normal curve up to z = 0.36; that is, find P(Z ≤ 0.36). Interpret this value.
4. Basing your estimate of future-Period monthly return parameters on the sample Meat and standard deviation for the period January 1994 to December 1996, construct a 90 percent confidence interval for the monthly return on a large-cap blend fund. Assume fund returns are normally distributed.
5. Basing your estimate of future-period monthly return parameter on the sample mean and standard deviation for the period January 1994 to December 1996, calculate the probability that a large-cap growth fund will earn a monthly return of 0 paean or less. Assume fund returns are normally distributed.
6. The basic calculation for volatility (denoted 0) as used in option pricing is the annualized standard deviation of continuously compounded daily returns. Calculate volatility for Dollar General Corporation (NYSE: DG) based on its closing prices for two weeks, given in the table below. (Annualize based on 250 days in a year.)
Dollar General Corporation Daily Closing Stock Price
| Date |
Closing Price ($) |
| 27 January- 2003 |
10.68 |
| 28 January. 2003 |
10.87 |
| 29 January 2003 |
11.00 |
| 30 January 2003 |
10.95 |
| 31 January 2003 |
11.26 |
| 3 February 2003 |
11.31 |
| 4 February 2003 |
11.23 |
| 5 February 2003 |
10.91 |
| 6 February 2003 |
10.80 |
| 7 February 2003 |
10.47 |