A62 ODD ANSWERS 27. (a) x P(x) 0 0.009 1 0.060 2 0.174 3 0.279 4 0.268 5 0.154 6 0.049 7 0.007 (b) Number of applicants Probability 0.05 0.10 0.15 0.20 0.25 0.30 0 1 2 3 4 5 6 7 Pennsylvania State University Applicant Acceptance Rate P(x) x Bell Shape (c) The following values are unusual: 0, 6 and 7. This is because their probabilities are all less than or equal to 0.05. 29. (a) x P(x) 0 0.00064 1 0.01077 2 0.07214 3 0.24151 4 0.40426 5 0.27068 (b) Number of adults Probability 0.35 0.30 0.40 0.25 0.20 0.15 0.10 0.05 0.45 1 2 3 5 0 4 Living to Age 100 P(x) x Skewed left (c) The values 0 and 1 are unusual because their probabilities are less than 0.05. 31. m ≈ 1.98, s 2 ≈ 1.33, s ≈ 1.15. On average, 1.98 out of every 6 penalty shots are converted. The standard deviation is 1.15, so most samples of 6 penalty shots would differ from the mean by at most 1.15. Unusual values would be any above 4.28. 33. m ≈ 6.3; s 2 ≈ 1.3; s ≈ 1.2. On average, 6.3 out of every 8 adults believe that life on other planets is possible. The standard deviation is 1.2, so most samples of 8 adults would differ from the mean by at most 1.2 adults. Unusual values would be any under 3.9. 35. m ≈ 3.72, s 2 ≈ 2.57, s ≈ 1.60. On average, 3.72 out of every 12 U.S. employees who are late for work blame oversleeping.The standard deviation is 1.60, so most samples of 12 U.S. employees who are late for work would differ from the mean by at most 1.60. Unusual values would be any under 0.52 or over 6.92. 37. (a) 0.102 (b) 0.042; unusual because it is less than or equal to 0.05 (c) 0.143 39. 0.033 41. (a) 0.107 (b) 0.107 (c) The results are the same. Section 4.2 Activity (page 214) 1 – 3. Answers will vary. Section 4.3 (page 220) 1. 0.080 3. 0.062 5. 0.175 7. 0.223 9. In a binomial distribution, the value of x represents the number of successes in n trials. In a geometric distribution, the value of x represents the first trial that results in a success. 11. (a) 0.190 (b) 0.154 (c) 0.082 13. (a) 0.195 (b) 0.433 (c) 0.567 15. (a) 0.227 (b) 0.878 (c) 0.122 17. (a) 0.232 (b) 0.406 (c) 0.950 19. (a) 0.298 (b) 0.463 (c) 0.537 21. (a) 0.064 (b) 0.556 (c) 0.016; unusual 23. (a) 0.071 (b) 0.827 (c) 0.173 25. (a) 0.002; unusual (b) 0.006; unusual (c) 0.980 27. (a) 0.12542 (b) 0.12541. The results are approximately the same. 29. (a) m = 1000; s 2 = 999,000; s ≈ 999.5 (b) 1000 times (c) Lose money. On average, you would win $500 once in every 1000 times you play the lottery. So, the net gain would be -$500. 31. (a) s 2 = 3.9, s ≈ 1.97. The standard deviation is about 1.97, so most of the scores will differ from the mean by no more than 2 strokes. (b) More than 8 strokes would be unusual. Uses and Abuses for Chapter 4 (page 223) 1. 11 incidents. The probability of 11 incidents is about 0.119, while the probability of at least 16 is about 0.093. 2. 10 to 12. The probability of 10 to 12 incidents is about 0.348, while the probability of less than ten incidents is about 0.341. 3. Yes. On holidays the fire department should adjust the guidelines because more people are out. Review Exercises for Chapter 4 (page 225) 1. Discrete. The grade of an exam is a random variable that can be counted. 3. (a) x P(x) 0 0.207 1 0.443 2 0.236 3 0.086 4 0.021 5 0.007 (b) Number of hits Probability 0.1 0 1 2 3 4 5 Hits per Game 0.2 0.3 0.4 0.5 P(x) x Skewed right 5. Yes 7. (a) m ≈ 2.8; s 2 ≈ 1.7; s ≈ 1.3 (b) The mean is 2.8, so the average number of cell phones per household is about 3. The standard deviation is 1.3, so most of the households differ from the mean by no more than about 1 cell phone. 9. -$3.13 11. Binomial experiment; Success: a green candy is selected; n = 12, p = 0.125, q = 0.875, x = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
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