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WARM UP :

Steps to perform simulations using digits: Assign digits to represent an outcome. Describe the scheme you will use to carry out this exp. Identify the Response. Perform simulation and Describe your Stopping Rule. State your conclusions. WARM UP :

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WARM UP :

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  1. Steps to perform simulations using digits: • Assign digits to represent an outcome. • Describe the scheme you will use to carry out this exp. • Identify the Response. • Perform simulation and Describe your Stopping Rule. • State your conclusions. WARM UP: Suppose that 80% of Texans prefer Dr. Pepper over Coke. Describe and carry out a simulation to determine the probability of selecting 3 people who all like Dr. Pepper. Use 10 trials. • Using: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Let 0 – 7 represent a person who prefers Dr. Pepper, 8, 9 = Likes Coke. • Use the Randomness to select 3 digits at a time. • The response is finding 3 out of 3 Dr. Pep. lovers, or NOT. • Stop when you select your 10th triplet. • Answer = ____________%

  2. EXAMPLE 2: Suppose that 35% of the computer chips in a shipment are defective. Describe and carry out a simulation representing 20 experimental units. • Using: 00 – 99, Let 00 – 34 represent a Defective Computer Chip, 35 - 99 = Good Chips. • Use the Random Digit table and take two digits at a time. • The Response is finding a defective chip or NOT. • Stop when you have came across 20 double digits • Answer = _____________

  3. SIMULATION The imitation of chance behavior, based on a model that accurately reflects the experiment under consideration, is called a simulation.

  4. Let 0 represent envelope with score > 1800 Let 1-9 represent envelope with score < 1800 the number of envelopes required would be about 30.

  5. HW: Page 267: 30, 22` 30. The World Series. Generate pairs of random digits 00-99. Let 00-54 represent a win by the favored team, and let 55-99 represent a win by the underdog. A trial consists of generating pairs until one team has 4 simulated wins. The response variable is whether or not the underdog wins. Theoretically the underdog is expected to win the World Series about 39% of the time.

  6. #22. Blood donors. One donor: Use digits 00-99. Let 00-43 represent a type O donor, and let 44-99 represent a donor who is not type O. Response variable is the number of pairs of digits generated until 3 type O donors are simulated. Once 3 type O donors are simulated, the trial is over. Theoretically, about 6.8 donors are required to be reasonably assured of getting 3 type O donors.

  7. #21. One attempt: Use 00-99 Let 01-72 represent making the shot and let 73-99, 00 represent missing the shot. Trial = shot until you miss or until you make 2 shots. Response= average number of points Theoretically, the player is expected to score about 1.24 points.

  8. Use double digits 00-99: Let 00-78 represent tires lasting longer that 30000 miles Let 79-99 represent tires NOT lasting longer that 30000 miles Response: 4 out of 4 tires last longer that 30000 miles.

  9. 23. Free groceries. One card with the prize indicated: Use digits 00-99. Let 01-10 represent $200, let 11-20 represent $100, let 21-40 represent $50, and let 41-99 and 00 represent $20. Repeated pairs of digits must be ignored. A trial continues until the total simulated prize is greater than $500. The response variable is the number of simulated customers until the payoff is greater than $500. Theoretically, about 10.2 winners are expected each week.

  10. 24. Find the ace. A component is turning over one card. One way to model the cards turned over is to generate random digits 0-9. Let the digit 0 represent the ace, and let digits 1, 2, 3, and 4 each represent one of the other four cards. Ignore digits 5-9. A trial consists of simulating turning over the cards until the ace is drawn. Each card must be represented individually; repeated digits must be ignored. The response variable is the number of simulated cards drawn until the ace is drawn, with $100 being awarded if the ace is drawn first, and $50, $20, $10, or $5 if the ace is drawn second, third, fourth, or fifth, respectively. The simulated average dollar amount of music the store is expected to give away is the total dollar amount of music given away divided by the number of trials. According to the simulation, the dollar amount given away is expected to be about $37.

  11. 25. Each child is a component. One way to model the component is to generate random digits 0-9. Let 0-4 represent a boy and let 5-9 represent a girl. A trial consists of generating random digits until a child of each gender is simulated. The response variable is the number of children simulated until this happens. The simulated average family size is the number of digits generated in each trial divided by the total number of trials. According to the simulation, the expected number of children in the family is about 3.

  12. It’s Not Easy Being Random

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