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Run a simulation to determine if buying 23 boxes is unusual

Run a simulation to determine if buying 23 boxes is unusual

Chemistry
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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Run a simulation to determine if buying 23 boxes is unusual

下午6:44 12月13日周一 * 100% Q AA ... 298 СНАРТER 5 PROBABILITY: WHAT ARE THE CHANCES? STATE: What is the probability that it will take 23 or more boxes to get a full set of 5 NASCAR collectible cards? PLAN: We need five numbers to represent the five possible cards. Let's let 1 = Jeff Gordon; 2 = Dale Earnhardt, Jr.; 3 = Tony Stewart; 4 = Danica Patrick; and 5 = Jimmie Johnson. We'll use randlnt(1,5) to simulate buying one box of cereal and looking at which card is inside. Because we want a full set of cards, we'll keep pressing Enter until we get all five of the labels from 1 to 5. We'll record the number of boxes that we had to open. GO Dadd. pil 1 DO: It's time to perform many repetitions of the simulation. Here are our first few L'ID SUPPORT Neescale Duralast results: Rep 1: 352152 354 9 boxes Rep 3: 5552412153 10 boxes Rep 5: 3322124 33 4 223332 3 3 4 2 25 22 boxes Rep 2: 51251414 12224453 16 boxes Rep 4: 435351115315452 15 boxes The Fathom dotplot shows the number of boxes we had to buy in 50 repetitions of the simulation. NASCAR cereal problem Dot Plot : 10 15 20 25 Boxes CONCLUDE: We never had to buy more than 22 boxes to get the full set of NASCAR drivers' cards in 50 repetitions of our simulation. So our estimate of the probability that it takes 23 or more boxes to get a full set is roughly 0. The NASCAR fan should be surprised by how many boxes she had to buy. For Practice Try Exercise 25 In the golden ticket lottery example, we ignored repeated numbers from 01 to 95 within a given repetition. Thať's because the chance process involved sampling students without replacement. In the NASCAR example, we allowed repeated numbers from 1 to 5 in a given repetition. That's because we are selecting a small number of cards from a very large population of cards in thousands of cereal box- es. So the probability of getting, say, a Danica Patrick card in the next box of cereal is still very close to 1/5 even if we have already selected a Danica Patrick card. What don't these simulations tell us? For the golden ticket parking lottery, we concluded that it's plausible the drawing was done fairly. Does that mean the lottery was conducted fairly? Not necessarily. All we did was estimate that the probability of getting two winners from the AP® Statistics class was about 10% if the drawing was fair. So the result isn't unlikely enough to convince us that the lottery was rigged. What about the cereal box simulation? It took our NASCAR fan 23 boxes to complete the set of 5 cards. Does that mean the company didn't THINK ABOUT IT 298 / 812 > 000 0000000 .... 00000F5 r OUR
Transcribed Image Text:下午6:44 12月13日周一 * 100% Q AA ... 298 СНАРТER 5 PROBABILITY: WHAT ARE THE CHANCES? STATE: What is the probability that it will take 23 or more boxes to get a full set of 5 NASCAR collectible cards? PLAN: We need five numbers to represent the five possible cards. Let's let 1 = Jeff Gordon; 2 = Dale Earnhardt, Jr.; 3 = Tony Stewart; 4 = Danica Patrick; and 5 = Jimmie Johnson. We'll use randlnt(1,5) to simulate buying one box of cereal and looking at which card is inside. Because we want a full set of cards, we'll keep pressing Enter until we get all five of the labels from 1 to 5. We'll record the number of boxes that we had to open. GO Dadd. pil 1 DO: It's time to perform many repetitions of the simulation. Here are our first few L'ID SUPPORT Neescale Duralast results: Rep 1: 352152 354 9 boxes Rep 3: 5552412153 10 boxes Rep 5: 3322124 33 4 223332 3 3 4 2 25 22 boxes Rep 2: 51251414 12224453 16 boxes Rep 4: 435351115315452 15 boxes The Fathom dotplot shows the number of boxes we had to buy in 50 repetitions of the simulation. NASCAR cereal problem Dot Plot : 10 15 20 25 Boxes CONCLUDE: We never had to buy more than 22 boxes to get the full set of NASCAR drivers' cards in 50 repetitions of our simulation. So our estimate of the probability that it takes 23 or more boxes to get a full set is roughly 0. The NASCAR fan should be surprised by how many boxes she had to buy. For Practice Try Exercise 25 In the golden ticket lottery example, we ignored repeated numbers from 01 to 95 within a given repetition. Thať's because the chance process involved sampling students without replacement. In the NASCAR example, we allowed repeated numbers from 1 to 5 in a given repetition. That's because we are selecting a small number of cards from a very large population of cards in thousands of cereal box- es. So the probability of getting, say, a Danica Patrick card in the next box of cereal is still very close to 1/5 even if we have already selected a Danica Patrick card. What don't these simulations tell us? For the golden ticket parking lottery, we concluded that it's plausible the drawing was done fairly. Does that mean the lottery was conducted fairly? Not necessarily. All we did was estimate that the probability of getting two winners from the AP® Statistics class was about 10% if the drawing was fair. So the result isn't unlikely enough to convince us that the lottery was rigged. What about the cereal box simulation? It took our NASCAR fan 23 boxes to complete the set of 5 cards. Does that mean the company didn't THINK ABOUT IT 298 / 812 > 000 0000000 .... 00000F5 r OUR
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