13.14: Problems
- Page ID
- 94715
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1.
You purchased 1,000 shares of a stock for $12 per share. Then, two months later, you purchased an additional 500 shares of the same stock at $9 per share. Calculate the weighted mean of the purchase price for the total of 1,500 shares.
2.
You score a 60 on a biology test. The mean test grade is 70, and the standard deviation is 5. Calculate and interpret your corresponding z-score.
3.
You score a 60 on a biology test. The mean test grade is 70, and the standard deviation is 5. What percentile does your grade correspond to?
4.
A fast food restaurant has measured service time for customers waiting in line, and the service time follows an exponential distribution with a mean waiting time of 1.9 minutes. The restaurant has a guarantee that if customers wait in line for more than 5 minutes, their meal is free. What is the probability that a customer will receive a free meal?
5.
The total value of your portfolio consists of approximately 65% stock assets, 25% bonds, and 10% cash equivalents. Historical returns have shown that stocks provide a return of 12%, bonds provide a return of 3.5%, and cash savings provide a return of 1.5%. What is the expected value of the return on this portfolio?
6.
The distribution of the average annual return of the S&P 500 over a 50-year time period follows a normal distribution with a mean rate of return of 10.5% and a standard deviation of 14.3%. What is the probability that an average annual return will fall between -3.8% and 24.8%?
7.
Write a short R program to find the expected return for the data set in the table below.
| Historical Return on United Airlines Stock | Associated Probability |
| 12% | 15% |
| 5% | 35% |
| 2% | 25% |
| -5% | 14% |
| -10% | 11% |