APPENDIX D 777 highly unlikely and is significantly low. Because we did get the sample mean of 97.49°F from Data Set 5, we have strong evidence suggesting that the assumed population mean of 98.6°F is likely to be wrong. 11. Sample statistics: n = 15, x = 62.7 seconds, s = 19.5 seconds. Generate random samples from a normally distributed population with the assumed mean of 60 seconds, a standard deviation of 19.5 seconds, and a sample size of n = 15. Answers vary, but here is a typical result: Among 100 generated samples, the sample mean of x = 62.7 seconds or higher occurred 33 times, so 62.7 seconds is not significantly high. The sample mean of 62.7 seconds could easily occur with a population mean of 60 seconds, so there isn’t strong evidence against 60 seconds as the population mean. 13. With switching, P1win2 = 2>3. With sticking, P1win2 = 1>3. 15. The reasoning is not correct. The proportion of girls will not increase. Chapter 4: Quick Quiz 1. 0.2 or 1>5 2. 4>5 or 0.8 3. 1>365 4. 1>100 or 0.01 5. Answer varies, but the probability should be somewhat low, such as 0.02. 6. 0.0680 7. 0.727 8. 0.00874 9. 0.00459 10. 0.0131 Chapter 4: Review Exercises 1. 0.684, which does not appear to be reasonably close to the proportion of females in the general population. It does not seem that the study subjects were randomly selected from the general population. 2. 0.125 3. 0.739 4. 0.714 5. 0.401 6. 0.0133 7. 0.0134 8. L is the event of randomly selecting one of the study subjects and getting someone who does not write with their left hand. P1L2 = 0.884. 9. M is the event of randomly selecting one of the study subjects and getting someone who is not a male. P1M2 = 0.684. 10. 0.00151. Yes, because the probability of getting three lefties is so small. 11. 115>652114>642113>632112>622 = 32,760>16,248,960 = 0.00202. Because that probability is so low, it is very unlikely that the seats were randomly assigned. 12. a. 0.25 b. 0.316 c. A result of x successes among n trials is a significantly high number of successes if the probability of x or more successes is unlikely with a probability of 0.05 or less. That is, x is a significantly high number of successes if P(x or more) … 0.05. (The value 0.05 is not absolutely rigid. Other values, such as 0.01, could be used to distinguish between results that are significant and those that are not significant.) d. No, the probability of getting all four people using vision correction is 0.316, which is not unlikely with a small probability such as 0.05 or less. Because the probability of four people using vision correction is so high, that event can easily occur and it is not a significant event. Section 4-4 1. The symbol ! is the factorial symbol, which represents the product of decreasing whole numbers, as in 5! = 5# 4# 3# 2# 1 = 120. Five NBA players can stand in line 120 different ways. 3. Because repetition is allowed, numbers are selected with replacement, so the combinations rule and the two permutation rules do not apply. The multiplication counting rule can be used to show that the number of possible outcomes is 10# 10# 10 = 1000. 5. 1>10,000 7. 1>190 9. 50,400; 1>50,400 11. 1>5,527,200 13. 1>100,000,000. No, there are far too many different possibilities. 15. 360; 1>360 (RHYTHM) 17. 1>292,201,338 19. 1>100,000 21. Area codes: 792. Phone numbers: 6,272,640,000. Yes. (With a total population of about 400,000,000, there would be roughly 16 phone numbers for every adult and child.) 23. a. 360,360 b. 3003 c. 1>3003 25. a. 1,048,576 b. 184,756 c. 0.176 d. With a probability of 0.176, the result is common, but it should not happen consistently. 27. 653,837,184,000 29. a. 1>302,575,350 b. There is a much better chance of being struck by lightning. c. Probability for the old Mega Millions game: 1>258,890,850. The current Mega Millions game has a substantially lower probability of winning when compared to the old Mega Millions game. 31. There are 62 different possible characters. The alphabet requires 26 characters and there are 10 digits, so the Morse code system is more than adequate. 33. 12 35. a. 1>177,100 b. $88,550 c. No, because the jackpot is too small. 37. 2,095,681,645,538 (about 2 trillion) 39. 0.000000112 3from 120C102>180C1024 Section 4-5 1. No. The generated numbers between 2 and 12 would be equally likely, but they are not equally likely with actual dice. 3. Yes, it does. Each of the 365 birthdays has the same chance of being selected, and the cards are replaced, so it is possible to select the same birthday more than once. 5. Randomly generate 50 integers, with each integer between 1 and 100. Consider the numbers 1 through 95 to be adults who recognize the brand name of McDonald’s, while the numbers 96 through 100 represent adults who do not recognize McDonald’s. 7. Randomly generate an integer between 1 and 1000 inclusive. Consider an outcome of 1 through 640 to be a pass that was caught and consider an outcome between 641 and 1000 to be a pass that was not caught. 9. Answers vary, but here is a typical result: Among 100 generated samples, the sample mean of x = 97.49°F or lower never occurred, so the conclusions are essentially the same as in Example 1: With the assumption that the mean body temperature is 98.6°F, we have found that the sample mean of 97.49°F is
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