Math & Stats for Business
1. This assignment is to be done individually . This is not a group assignment.
1. The homework assignment is due in the beginning of the next class. Please bring a hard copy with you to the class.
1. If you have difficulty printing the assignment, please email the assignment to the instructor before the class.
1. Late or redone homework assignments will be accepted only at the final class (up to a total of two).
1. Only explained and detailed answers will be accepted.
1. During one holiday season, the Texas lottery played a game called the Stocking Stuffer. With this game, total instant winnings of $34.8 million were available in 70 million $1 tickets, with ticket pr4izes ranging from $1 to $1,000.
Shown here are the various prizes and the probability of winning each prize. Use these data to compute the expected value of the game, the variance of the game, and the standard deviation of the game. (8 points)
| Prize (x) | Probability P(x) |
| $1,000 | .00002 |
| 100 | .00063 |
| 20 | .00400 |
| 10 | .00601 |
| 4 | .02403 |
| 2 | .08877 |
| 1 | .10479 |
| 0 | .77176 |
2. The following data are the result of a historical study of the number of flaws found in a porcelain cup produced by a manufacturing firm. Use these data and the associated probabilities to compute the expected number of flaws and the standard deviation of flaws. (7 points)
| Flaws | Probability |
| 0 | .461 |
| 1 | .285 |
| 2 | .129 |
| 3 | .087 |
| 4 | .038 |
3. Determine the mean, variance, and standard deviation of the following discrete distribution. (5 points)
| X | P(x) |
| 1 | .238 |
| 2 | .280 |
| 3 | .177 |
| 4 | .158 |
| 5 | .137 |