Birdville ISD / Overview
right321945The imitation of chance behavior, based on a model that accurately reflects the situation, is called a simulation. Follow the 4-step process: State: Ask a question of interest about some chance process. Plan: Describe how to use a chance device (random digit table, randInt command in calculator) to imitate one repetition of the process. Don’t forget to determine if repeating numbers are ok or not! Tell what you will record at the end of each repetition. Do: Perform many repetitions. (Use clear notation for grader to follow)Conclude: Use the results of your simulations to answer the question of interest. Don’t forget that the results you get is an estimation of the true proportion!00The imitation of chance behavior, based on a model that accurately reflects the situation, is called a simulation. Follow the 4-step process: State: Ask a question of interest about some chance process. Plan: Describe how to use a chance device (random digit table, randInt command in calculator) to imitate one repetition of the process. Don’t forget to determine if repeating numbers are ok or not! Tell what you will record at the end of each repetition. Do: Perform many repetitions. (Use clear notation for grader to follow)Conclude: Use the results of your simulations to answer the question of interest. Don’t forget that the results you get is an estimation of the true proportion!Chapter 5.1 - SimulationsEx 1) A basketball player makes 2/3 of his free throws. To simulate a single free throw, which of the following assignments of digits to making a free throw are appropriate? I. 0 and 1 correspond to making free throw and 2 corresponds to missing the free throw. II. 01, 02, 03, 04, 05, 06, 07, and 08 correspond to making a free throw and 09, 10, 11, and 12 correspond to missing the free throw. III. Use a die and let 1, 2, 3, and 4 correspond to making a free throw while 5 and 6 correspond to missing a free throw. a. I onlyb. II only c. III only d. I and IIIe. I, II, and IIIEx 2) In the game of Scrabble, each player begins by drawing 7 tiles from a bag containing 100 tiles. There are 42 vowels, 56 consonants, and 2 blank tiles in the bag. Kate chooses her 7 tiles and is surprised to discover that all of them are vowels. Should she be? Design and carry out a simulation to answer this question. Follow the four-step process. _______ 1.You want to use simulation to estimate the probability of getting exactly one head and one tail in two tosses of a fair coin. You assign the digits 0, 1, 2, 3, 4 to heads and 5, 6, 7, 8, 9 to tails. Using the following random digits to execute as many simulations as possible, what is your estimate of the probability? 19226 95034 05756 07118 a. 1/20b. 1/10c. 5/10d. 6/10e. 2/3 _______ 2. A box has 10 tickets in it, two of which are winning tickets. You draw a ticket at random. If it’s a winning ticket, you win. If not, you get another chance, as follows: your losing ticket is replaced in the box by a winning ticket (so now there are 10 tickets, as before, but 3 of them are winning tickets). You get to draw again, at random. Which of the following are legitimate methods for using simulation to estimate the probability of winning? I. Choose, at random, a two-digit number. If the first digit is 0 or 1, you win on the first draw; If the first digit is 2 through 9, but the second digit is 0, 1, or 2, you win on the second draw. Any other two-digit number means you lose. II. Choose, at random, a one-digit number. If it is 0 or 1, you win. If it is 2 through 9, pick a second number. If the second number is 8, 9, or 0, you win. Otherwise, you lose. III. Choose, at random, a one-digit number. If it is 0 or 1, you win on the first draw. If it is 2, 3, or 4, you win on the second draw; If it is 5 through 9, you lose. a. I onlyb. II onlyc. III onlyd. I and IIe. I, II, and IIIUse the following scenario for Questions 3 and 4: To simulate a toss of a coin we let the digits 0, 1, 2, 3, and 4 correspond to a head and the digits 5, 6, 7, 8, and 9 correspond to a tail. Consider the following game: We are going to toss the coin until we either get a head or we get two tails in a row, whichever comes first. If it takes us one toss to get the head we score 2 points, if it takes us two tosses we score 1 point, and if we get two tails in a row we score 0. Use the following sequence of random digits to simulate this game as many times as possible. 12975 13258 45144_______ 3. Based on your simulation, the estimated probability of scoring 2 points in this game isa. 1/4 b. 5/15 c. 7/15 d. 9/15 e. 7/11_______ 4. Based on your simulation, the estimated probability of scoring zero is a. 1/2 b. 2/11 c. 2/15 d. 6/15 e. 7/115. In the United Kingdom’s Lotto game, a player picks six numbers from 1 to 49 for each ticket. Rosemary bought one ticket for herself. She had the lottery computer randomly select the six numbers. When the six winning numbers were drawn, Rosemary was surprised to find that none of these numbers appeared on the Lotto ticket she had bought. Should she be? Design and carry out a simulation using the RandInt command in your calculator to answer this question. Follow the four-step process. 6. According to New Jersey Transit, the 8:00 am weekday train from Princeton to New York City has a 90% chance of arriving on time. To test this claim, an auditor chooses 6 weekdays at random during a month to ride this train. The train arrives late on 2 of those days. Does the auditor have convincing evidence that the company’s claim isn’t true? Design and carry out a simulation using Table D (start at line 101) to estimate the probability that a train with a 90% chance of arriving on time each day would be late 2 or more of 6 days. Follow the four-step process. ................
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