ODD ANSWERS A65 11. (a) m = 53.2, s ≈ 19.9 (b) Sample Mean 19, 19 19 19, 48 33.5 19, 56 37.5 19, 64 41.5 19, 79 49 48, 19 33.5 48, 48 48 48, 56 52 48, 64 56 48, 79 63.5 56, 19 37.5 56, 48 52 56, 56 56 56, 64 60 56, 79 67.5 64, 19 41.5 64, 48 56 64, 56 60 64, 64 64 64, 79 71.5 79, 19 49 79, 48 63.5 79, 56 67.5 79, 64 71.5 79, 79 79 (c) mx = 53.2, sx ≈ 14.1 The means are equal, but the standard deviation of the sampling distribution is smaller. 13. (a) m = 389, s ≈ 28.65 (b) Sample Mean 350, 350, 350 350 350, 350, 399 366.33 350, 350, 418 372.67 350, 399, 350 366.33 350, 399, 399 382.67 350, 399, 418 389 350, 418, 350 372.67 350, 418, 399 389 350, 418, 418 395.33 399, 350, 350 366.33 399, 350, 399 382.67 399, 350, 418 389 399, 399, 350 382.67 399, 399, 399 399 399, 399, 418 405.33 399, 418, 350 389 399, 418, 399 405.33 399, 418, 418 411.67 418, 350, 350 372.67 418, 350, 399 389 418, 350, 418 395.33 418, 399, 350 389 418, 399, 399 405.33 418, 399, 418 411.67 418, 418, 350 395.33 418, 418, 399 411.67 418, 418, 418 418 (c) mx = 389, sx ≈ 16.54 The means are equal, but the standard deviation of the sampling distribution is smaller. 15. 0.9726; not unusual 17. 0.0351 (Tech: 0.0349); unusual 19. mx = 31.58, sx = 1.419 21. mx = 97.2, sx = 0.138 x Mean day-ahead price for renewable energy (in euros per mega-watt hour) 28.5 30 31.5 33 34.5 x Mean female body temperature (in Fahrenheit) 96.92 97.06 97.2 97.34 97.48 23. mx = 54,000, sx = 1886.48 x Mean salary (in dollars) 50,000 52,000 54,000 56,000 58,000 25. mx = 603, sx = 27.75 x Mean score 545 560 575 590 605 620 635 650 665 27. n = 40: mx = 603, sx = 17.55 n = 60: mx = 603, sx = 14.33 x Mean score 545 575 605 635 665 As the sample size increases, the standard deviation of the sample means decreases, while the mean of the sample means remains constant. 29. 0.3939 (Tech: 0.3927). About 39% of samples of 32 years will have an annual mean gain between 400 and 700. 31. 0.0110 (Tech: 0.0109). About 1.1% of samples of 30 U.S. states will have a mean asthma rate greater than 10%. 33. It is more likely to select a sample of 10 states with a mean asthma prevalence of less than 10% because the sample of 10 states has a higher probability. 35. Yes, it is very unlikely that you would have randomly sampled 40 cans with a mean equal to 127.9 ounces because it is more than 3 standard deviations from the mean of the sample means. 37. (a) 0.3085 (b) 0.0008 39. Yes, the finite correction factor should be used. 0.06615 (Tech: 0.06614) 41. 0.0446 (Tech: 0.0448). The probability that less than 55% of a sample of 105 residents are in favor of building a new high school is about 4.5%. Because the probability is less than 0.05, this is an unusual event. Section 5.4 Activity (page 274) 1 – 2. Answers will vary. Section 5.5 (page 281) 1. Cannot use normal distribution 3. Cannot use normal distribution
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