752 CHAPTER 11 Probability haircut. One day, Marcus gives haircuts to 12 customers. What is the probability that exactly 9 of his customers tip him when they are paying for their haircut? 0.25810 19. Auto Insurance The Truman Insurance company reported that 60% of all automobile damage claims were made by people under the age of 25. If eight automobile damage claims were randomly selected, determine the probability that exactly five of them were made by someone under the age of 25. 0.27869 20. Bank Loans Records from Cajero Bank show that 70% of car loan applications are approved. If eight car loan applications from this bank are randomly selected, determine the probability that exactly five of the applications are approved. 0.25412 21. Dolphin Drug Care When treated with the antibiotic resonocyllin, 92% of all dolphins are cured of brucellosis. If six dolphins with brucellosis are treated with resonocyllin, determine the probability that exactly four are cured. 0.06877 22. Medical Research When treated with a new drug to treat Crohn’s disease, 80% of all patients saw an improvement in their symptoms. If 25 patients are treated with the new drug, determine the probability that 20 will see an improvement in their symptoms. 0.19602 23. Cricket Bats D’Yard Corporation makes cricket bats. The quality control manager determines that 99.0% of the bats made at D’Yard meet the International Cricket Council (ICC) safety standards. Montgomery College wishes to purchase 100 bats. What is the probability that all 100 meet the ICC safety standards? 0.36603 24. Quality Improvement See Exercise 23. After undergoing a quality improvement program, D’Yard improves the bat quality, so that 99.9% of the bats made meet ICC safety standards. What is the probability that of the next 100 bats produced, all 100 meet the ICC safety standards? 0.90479 25. Multiple-Choice Quiz DJ is taking a 10-question, multiplechoice quiz. He has not studied and will be guessing on each of the questions. Each question has 5 choices. Determine the probability that DJ correctly answers a) 5 questions 0.02642 b) 0 questions 0.10737 c) at least 1 question 0.89263 26. Multiple-Choice Quiz See Exercise 25. Suppose DJ can eliminate one of the choices in each of the 10 questions and then makes a guess among the remaining 4 choices. Determine the probability that DJ correctly answers a) 5 questions 0.05840 b) 0 questions 0.05631 c) at least 1 question 0.94369 Challenge Problems/Group Activities In Exercises 27–29, when necessary, round answers to 5 decimal places. 27. Selecting 6 Cards Six cards are randomly selected from a standard 52-card deck with replacement. Determine the probability that a) exactly three face cards are obtained. 0.11188 b) exactly two spades are obtained. 0.29663 28. Office Visit The probability that a person visiting Dr. Suarez’s office is more than 60 years old is 0.7. Determine the probability that a) exactly three of the next five people visiting the office are more than 60 years old. 0.3087 b) at least three of the next five people visiting the office are more than 60 years old. 0.83692 29. Candies A bag of colorful candies consists of 24% blue candies, 20% orange candies, 16% green candies, 14% yellow candies, 13% red candies, and 13% brown candies. If 10 candies are randomly selected from the bag, determine the probability that at least one of the candies is a) blue. 0.93571 b) orange. 0.89263 c) green. 0.82510 d) yellow. 0.77870 e) red. 0.75158 f) brown. 0.75158 Philip Scalia/Alamy Stock Photo Angelina Zinovieva/ Shutterstock
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