Bluman A.G. Elementary Statistics- A Step By Step Approach

Section 14–3 Simulation Techniques and the Monte Carlo Method 7457. What happens when the number of repetitions isincreased? When the repetitions increase, there is a higherprobability that the simulation will yield more precise answers.For Exercises 8 through 13, explain how eachexperiment can be simulated by using random numbers.8. Foreign-Born Residents Almost 16% of Texasresidents are foreign-born. Explain how to select asample of 40 based on this scenario.Source: factfinder.census.gov9. Stay-at-Home Parents Fewer than one-half of allmothers are stay-at-home parents. Recent statisticsindicate that 68.1% of all mothers with children underage 18 are in the labor force. Explain how to create asimulation to represent this situation.Source: New York Times Almanac.10. Playing Basketball Two basketball players have afree-throw contest—one is a 70% shooter and the otheris a 75% shooter. They each shoot 20 shots in groups of5 shots each. Use a calculator to simulate the contestand find out who wins. (Repeat a number of times andcompare your answers.)11. Television Set Ownership Thirty-five percent of U.S.households with at least one television set havepremium cable service. Explain how to simulate thiswith random numbers. Use your method to select arandom sample of 100 households and test thehypothesis that p does not equal 35%.12. Matching Pennies Two players match pennies. Use theodd digits to represent a match and the even digits to represent anonmatch.13. Odd Man Out Three players play odd man out. (Threecoins are tossed; if all three match, the game is repeatedand no one wins. If two players match, the third personwins all three coins.) Let an odd number represent heads andan even number represent tails. Then each person selects a digit atrandom.For Exercises 14 through 21, use random numbers tosimulate the experiments. The number in parenthesesis the number of times the experiment should be repeated.14. Tossing a Coin A coin is tossed until four heads areobtained. Find the average number of tosses necessary.(50) Answers will vary.15. Rolling a Die A die is rolled until all faces appear atleast once. Find the average number of tosses. (30)Answers will vary.16. Prizes in Caramel Corn Boxes A caramel corncompany gives four different prizes, one in each box.They are placed in the boxes at random. Find theaverage number of boxes a person needs to buy to getall four prizes. (40) Answers will vary.17. Keys to a Door The probability that a door is locked is0.6, and there are five keys, one of which will unlockthe door. The experiment consists of choosing one keyat random and seeing if you can open the door. Repeatthe experiment 50 times and calculate the empiricalprobability of opening the door. Compare your resultto the theoretical probability for this experiment.Answers will vary.18. Lottery Winner To win a certain lotto, a person mustspell the word big. Sixty percent of the tickets containthe letter b, 30% contain the letter i, and 10% containthe letter g. Find the average number of tickets a personmust buy to win the prize. (30) Answers will vary.19. Clay Pigeon Shooting Two shooters shoot claypigeons. Gail has an 80% accuracy rate and Paul has a60% accuracy rate. Paul shoots first. The first personwho hits the target wins. Find the probability that eachwins. (30). Answers will vary.20. In Exercise 19, find the average number of shotsfired. (30) Answers will vary.21. Basketball Foul Shots A basketball player has a 60%success rate for shooting foul shots. If she gets twoshots, find the probability that she will make one or bothshots. (50). Answers will vary.22. Which would be easier to simulate with randomnumbers, baseball or soccer? Explain. Answers will vary.23. Explain how cards can be used to generate randomnumbers. Answers will vary.24. Explain how a pair of dice can be used to generaterandom numbers. Answers will vary.Summary• To obtain information and make inferences about a large population, researchersselect a sample. A sample is a subgroup of the population. Using a sample rather thana population, researchers can save time and money, get more detailed information,and get information that otherwise would be impossible to obtain. (14–1)• The four most common methods researchers use to obtain samples are random,systematic, stratified, and cluster sampling methods. In random sampling, sometype of random method (usually random numbers) is used to obtain the sample. Insystematic sampling, the researcher selects every kth person or item after selectingthe first one at random. In stratified sampling, the population is divided into14–27