Page 1 > of 7 INTRODUCTION Probability problems are interesting statistics problems. One way to approach probability problems is to simulate an experiment many times to give an idea of what would happen and then make a decision based on the simulations. A simulation is a way to represent something without actually doing it. When the Air Force trains a new pilot, it does not give the new recruit a multi-million-dollar jet and say, "Let's see if you can get this baby off the ground. The new pilot is first trained using a machine that simulates flying Simulations are ways to represent the process of an actual experiment. The simulation and the real experiment would have similar outcomes and probabilities. In statistics probability problems, we use simulations to calculate outcomes and probabilities because repeatedly conducting actual experiments can be difficult or costly. Newsroom Staffing The manager of a local television newsroom relies on three top reporters. She relies on Abigail, Ben, and Shawn to assemble teams for breaking news stories. The trouble is that all three reporters spend most of their time out of the office. The reporters' jobs take them out of the office to research background information for ongoing news stories. But the manager feels it is important to have at least one of them in the newsroom at any given time. She would like to be reasonably sure that at least one of them will always be there. If this is not probable, then she may need to hire another reporter. Abigail is in the newsroom 40% of the time, Ben 60% of the time, and Shawn 10% of the time. Should the manager hire a new field reporter? To help the manager answer this question, we can design a simulation Use the random number table at the end of this lesson to simulate the reporters being in the office. To do this, pick three random digits. Begin anywhere you like in the table, and choose three consecutive digits from the table. Each digit represents a field reporter. For the first digit, we consider Abigail to be in the office of the random digit is 1, 2, 3, or 4. (Since she is in the office 40% of the time, choose four digits. You could choose any four digits, such as 1, 2, 3, 4 or 2,4,6,8. We chose the most simple.) . For the second digit, we consider Ben to be in the office if the digit is 1, 2, 3, 4, 5, or 6. (Since he is in the office 60% of the time, choose six digits.) For the third digit, we consider Shawn to be in the office if the digit is 1. (Since he is in the office 10% of the time, choose only one digit.) MacBook Pro og 57 50 59 FE FE A & S 4 3 5 6 7 8 9 0 E R T Y U 0 Page 1 . . To conduct one trial, choose three digits and check to see if at least one of the reporters is in the office. Record the results. Look at line 6 of the random number table. (We could begin at any randomly selected line in the table.) The first three digits are 2,3,5-2 means Abigail is in the office, 3 means Ben is in the office, and 5 means Shawn is out of the office. o The next three digits are 5, 6, 8-Ben is in the office, o The next three digits are 8,5,3-Ben is in the office. It looks as though the manager does not need to hire anyone. Think about the Law of Large Numbers. Have you done enough trials? 2 Continue the process: The next three digits are 8, 7,0-none of the reporters are in the office The next three digits are 9,5,1-Shawn is in the office. The next three digits are 6, 7,2-none of the reporters are in the office. A keep track of this information using a frequency distribution table. Continue through the next row or further as time allows Frequency Total Event At Least One Reporter in the Newsroom No Reporters in the Newsroom Total B Do you think the manager should hire another reporter? actores 30 DD 14 FS DI FE F90 51 & 3 $ 4 5 6 o * 7 8 9 0 E R. T Y U 0 of 7 ZOO Page 3 Lesson 6.1.4: Simulation TRY THESE 3 The Kalama Zoo houses nine orangutans-five males and four females. Orangutans are relatives of monkeys and gorillas. The zoo wants to know if a new diet supplement for the orangutans will be good for them to eat. To help find out, a trainer randomly selects three of these animals as an experimental group. The three selected orangutans will eat the new diet supplement. To properly run the experiment, the trainer has to move the three chosen orangutans to a newly constructed habitat. The next day, the trainer's boss finds three female orangutans in the new habitat. He is furious and threatens to fire the trainer. Why? It turns out that the males sometimes try to bite the trainer. His boss thinks the trainer just didn't want to be bitten, so he avoided selecting males for the experiment. Since the trainer only chose females for the experiment, the 200 may not learn whether the supplement is good for males. The trainer claims that he really did randomly select three females. Should the trainer be fired? Is it likely that the trainer could have selected three females using random selection Design a simulation to assist you in answering the question. MacBook Pro > of 7 Page of 7 Page of 7 INTRODUCTION Probability problems are interesting statistics problems. One way to approach probability problems is to simulate an experiment many times to give an idea of what would happen and then make a decision based on the simulations. A simulation is a way to represent something without actually doing it. When the Air Force trains a new pilot, it does not give the new recruit a multi-million-dollar jet and say, "Let's see if you can get this baby off the ground. The new pilot is first trained using a machine that simulates flying Simulations are ways to represent the process of an actual experiment. The simulation and the real experiment would have similar outcomes and probabilities. In statistics probability problems, we use simulations to calculate outcomes and probabilities because repeatedly conducting actual experiments can be difficult or costly. Newsroom Staffing The manager of a local television newsroom relies on three top reporters. She relies on Abigail, Ben, and Shawn to assemble teams for breaking news stories. The trouble is that all three reporters spend most of their time out of the office. The reporters' jobs take them out of the office to research background information for ongoing news stories. But the manager feels it is important to have at least one of them in the newsroom at any given time. She would like to be reasonably sure that at least one of them will always be there. If this is not probable, then she may need to hire another reporter. Abigail is in the newsroom 40% of the time, Ben 60% of the time, and Shawn 10% of the time. Should the manager hire a new field reporter? To help the manager answer this question, we can design a simulation Use the random number table at the end of this lesson to simulate the reporters being in the office. To do this, pick three random digits. Begin anywhere you like in the table, and choose three consecutive digits from the table. Each digit represents a field reporter. For the first digit, we consider Abigail to be in the office of the random digit is 1, 2, 3, or 4. (Since she is in the office 40% of the time, choose four digits. You could choose any four digits, such as 1, 2, 3, 4 or 2,4,6,8. We chose the most simple.) . For the second digit, we consider Ben to be in the office if the digit is 1, 2, 3, 4, 5, or 6. (Since he is in the office 60% of the time, choose six digits.) For the third digit, we consider Shawn to be in the office if the digit is 1. (Since he is in the office 10% of the time, choose only one digit.) MacBook Pro og 57 50 59 FE FE A & S 4 3 5 6 7 8 9 0 E R T Y U 0 Page 1 . . To conduct one trial, choose three digits and check to see if at least one of the reporters is in the office. Record the results. Look at line 6 of the random number table. (We could begin at any randomly selected line in the table.) The first three digits are 2,3,5-2 means Abigail is in the office, 3 means Ben is in the office, and 5 means Shawn is out of the office. o The next three digits are 5, 6, 8-Ben is in the office, o The next three digits are 8,5,3-Ben is in the office. It looks as though the manager does not need to hire anyone. Think about the Law of Large Numbers. Have you done enough trials? 2 Continue the process: The next three digits are 8, 7,0-none of the reporters are in the office The next three digits are 9,5,1-Shawn is in the office. The next three digits are 6, 7,2-none of the reporters are in the office. A keep track of this information using a frequency distribution table. Continue through the next row or further as time allows Frequency Total Event At Least One Reporter in the Newsroom No Reporters in the Newsroom Total B Do you think the manager should hire another reporter? actores 30 DD 14 FS DI FE F90 51 & 3 $ 4 5 6 o * 7 8 9 0 E R. T Y U 0 of 7 ZOO Page 3 Lesson 6.1.4: Simulation TRY THESE 3 The Kalama Zoo houses nine orangutans-five males and four females. Orangutans are relatives of monkeys and gorillas. The zoo wants to know if a new diet supplement for the orangutans will be good for them to eat. To help find out, a trainer randomly selects three of these animals as an experimental group. The three selected orangutans will eat the new diet supplement. To properly run the experiment, the trainer has to move the three chosen orangutans to a newly constructed habitat. The next day, the trainer's boss finds three female orangutans in the new habitat. He is furious and threatens to fire the trainer. Why? It turns out that the males sometimes try to bite the trainer. His boss thinks the trainer just didn't want to be bitten, so he avoided selecting males for the experiment. Since the trainer only chose females for the experiment, the 200 may not learn whether the supplement is good for males. The trainer claims that he really did randomly select three females. Should the trainer be fired? Is it likely that the trainer could have selected three females using random selection Design a simulation to assist you in answering the question. MacBook Pro > of 7 Page of 7 Page