776 APPENDIX D c. In this case, the results are the same when rounded to three significant digits, but with more significant digits, the results of 0.0108767364 and 0.0108657516 are different. 15. a. 0.0309. Yes, the events are independent. b. 0.0308. The events are dependent, not independent. 17. 731>8505 or 0.0859 19. 0.000118 21. a. 300 b. 154 c. 0.513 23. 0.990 25. a. 0.0366 b. 0.00133956 or 0.00134 rounded c. 0.000049027896 or 0.0000490 rounded d. By using one drive without a backup, the probability of total failure is 0.0366, and with three independent drives, the probability drops to 0.0000490 (rounded). By changing from one drive to three, the probability of total failure drops from 0.0366 to 0.0000490, and that is a very substantial improvement in reliability. Back up your data! 27. 0.838. The probability of 0.838 is high, so it is likely that the entire batch will be accepted, even though it includes many firmware defects. 29. a. 0.299 b. Using the 5% guideline for cumbersome calculations: 0.00239 [using the rounded result from part (a)] or 0.00238 31. a. 0.999775 b. 0.970225 c. The series arrangement provides better protection. 33. a. P1A or B2 = P1A2 + P1B2 - 2P1A and B2 b. 3210>8505 or 0.377 Section 4-3 1. The event of not getting at least 1 defect among the 4 calculators, which means that all 4 calculators are good. 3. The probability that the polygraph indicated a lie given that the subject did tell a lie. 5. 15>16 or 0.938 7. a. 0.488 b. 0.134 c. 0.116 d. 0.866 9. a. 0.999 b. 0.00100 11. 0.965. The probability is high enough so that she can be reasonably sure of getting a defect for her work. 13. a. 27>43 or 0.628 b. 16>43 or 0.372 c. It appears that when students are given four quarters, they are more likely to spend the money than keep it. 15. a. 27>43 or 0.628 b. 12>46 or 0.261 c. It appears that students are more likely to spend the money when given four quarters than when given a $1 bill. 17. 15>47 or 0.319. This is the probability of the polygraph making it appear that the subject lied when the subject did not lie, so the subject would be unfairly characterized as a liar. 19. 42>57 or 0.737. To be truly effective, the probability should be much higher. There is not sufficient evidence to conclude that the polygraph is effective. 21. a. 0.999851 b. 0.999998. The usual round-off rule for probabilities would result in a probability of 1.00, which would incorrectly indicate that we are certain to have at least one working hard drive. 23. 0.490. The probability is not low, so further testing of the individual samples will be necessary in 49% of the combined samples. 25. 0.569 Chapter 4 Answers Section 4-1 1. P1A2 = 1>10,000, or 0.0001. P1A2 = 9999>10,000, or 0.9999. 3. a. 1>6 or 0.167 b. 1>2or0.5 c. 0 5. 0, 3>5, 1, 0.135 7. 1>10 or 0.1 9. Neither significantly low nor significantly high 11. Significantly high 13. 1>2 or 0.5 15. 0.33 17. 1>10 or 0.1 19. 0 21. 239>291 or 0.821. Yes, the technique appears to be effective. 23. 428>580 or 0.738; yes 25. 0.730. The result suggests that it is likely for someone to use a social networking site. 27. a. brown>brown, brown>blue, blue>brown, blue>blue b. 1>4 c. 3>4 29. 3>8 or 0.375 31. 4>16 or 1>4 or 0.25. 33. Because the probability of a result such as 40 is small (less than or equal to 0.05), and because 40 is much higher than what is expected with randomness, the result of 40 is significantly high. 35. Because the probability of a result as low as 14 is 0.029792, that probability is small (less than or equal to 0.05). The result of 14 Democrats being placed on the first line is significantly low. 37. If pregnant women have no ability to predict the genders of their babies, then among 104 predictions, we expect about half of them (or 52) to be correct. The 57 correct predictions is greater than 52. The high probability of 0.189 is greater than 0.05, so 57 correct predictions is not significantly high (and it is not significantly low). It does not appear that pregnant women can correctly predict the genders of their babies. 39. Because the probability of getting 604 or more respondents who have made new friends online is 0.00000306 (less than or equal to 0.05), it appears that 604 is significantly high. This suggests that the true rate is not 50%. 41. a. 999:1 b. 499:1 c. Yes. If payoffs were made according to the actual odds, the payoff for a winning ticket would be a profit of $999 instead of only $499. 43. a. $5.80 b. 5.80:2 or 29:10 (or roughly 3:1) c. 4.168:1 (or roughly 4:1) d. $10.34 or about $10 (instead of the actual payoff of $7.80) Section 4-2 1. P1D2 represents the probability of selecting a smartphone with a manufacturing defect, and P1D2 represents the probability that the selected smartphone does not have a manufacturing defect. 3. Because the selections are made without replacement, the events are dependent. Because the sample size of 1068 is less than 5% of the population size of 30,488,983, the selections can be treated as being independent (based on the 5% guideline for cumbersome calculations). 5. 0.318; 0.5 7. 0.87 9. 887>8505 or 0.104 11. 3941>8505 or 0.463 13. a. 0.0109. Yes, the events are independent. b. 0.0109. The events are dependent, not independent.
RkJQdWJsaXNoZXIy NjM5ODQ=