Jerry is excited to go shoot clay pidgeons with some friends this weekend. He has been practicing and knows that he can hit the clays 79% of the time. His two buddies decided that the person who hits the most out of the next 17 will get treated to lunch. Andy just shot 8 clays, and Tim was able to hit 13. Here is Jerry's probability table: X PMF CDF 0 0 0 1 0 0 2 0 0 3 0 0 4 1.0E-6 2.0E-6 5 1.4E-5 1.6E-5 6 0.000105 0.000121 7 0.000623 0.000744 8 0.002929 0.003673 9 0.01102 0.014693 10 0.033165 0.047858 11 0.079395 0.127254 12 0.149339 0.276592 13 0.216076 0.492668 14 0.232245 0.724913 15 0.174737 0.899649 16 0.082168 0.981817 17 0.018183 1 Note: Report all probabilities in decimal form accurate to 3 places. Questions: First and foremost, Jerry doesn't want to embarrass himself. He just wants to beat out Andy. What is the probability that he will do better than 8? If Jerry were to do rounds of 17 clays repeatedly and average the results, what would his expected value be? Jerry really does want to get a free lunch. What is the probability that he does better than Tim? What is the probability that he does better than Andy, but worse than Tim? Peter is a friend who just likes to watch and place bets. Supposing he must select a value for the number of clays Jerry will break, how many breaks should he bet that Jerry will get this round of 17 clays if he wants the best chance to win his bet?
Jerry is excited to go shoot clay pidgeons with some friends this weekend. He has been practicing and knows that he can hit the clays 79% of the time. His two buddies decided that the person who hits the most out of the next 17 will get treated to lunch. Andy just shot 8 clays, and Tim was able to hit 13. Here is Jerry's probability table:
| X | PMF | CDF |
|---|---|---|
| 0 | 0 | 0 |
| 1 | 0 | 0 |
| 2 | 0 | 0 |
| 3 | 0 | 0 |
| 4 | 1.0E-6 | 2.0E-6 |
| 5 | 1.4E-5 | 1.6E-5 |
| 6 | 0.000105 | 0.000121 |
| 7 | 0.000623 | 0.000744 |
| 8 | 0.002929 | 0.003673 |
| 9 | 0.01102 | 0.014693 |
| 10 | 0.033165 | 0.047858 |
| 11 | 0.079395 | 0.127254 |
| 12 | 0.149339 | 0.276592 |
| 13 | 0.216076 | 0.492668 |
| 14 | 0.232245 | 0.724913 |
| 15 | 0.174737 | 0.899649 |
| 16 | 0.082168 | 0.981817 |
| 17 | 0.018183 | 1 |
Note: Report all probabilities in decimal form accurate to 3 places.
Questions:
First and foremost, Jerry doesn't want to embarrass himself. He just wants to beat out Andy. What is the probability that he will do better than 8?
If Jerry were to do rounds of 17 clays repeatedly and average the results, what would his expected value be?
Jerry really does want to get a free lunch. What is the probability that he does better than Tim?
What is the probability that he does better than Andy, but worse than Tim?
Peter is a friend who just likes to watch and place bets. Supposing he must select a value for the number of clays Jerry will break, how many breaks should he bet that Jerry will get this round of 17 clays if he wants the best chance to win his bet?
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