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Chapter 14: Q3BSC (page 654)
Control Limits In constructing a control chart for the proportions of defective dimes, it is found that the lower control limit is -0.00325. How should that value be adjusted?
The value of the lower control limit should be adjusted to 0.
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Heights On the basis of Data Set 1 “Body Data” in Appendix B, assume that heights of men are normally distributed, with a mean of 68.6 in. and a standard deviation of 2.8 in.
a. The U.S. Coast Guard requires that men must have a height between 60 in. and 80 in. Findthe percentage of men who satisfy that height requirement.
b. Find the probability that 4 randomly selected men have heights with a mean greater than 70 in.
Internet Doctors: Graph The accompanying graph was created to depict the results of the survey described in Exercise 1. Is the graph somehow misleading? If so, how?
Energy Consumption. Exercises 1–5 refer to the amounts of energy consumed in the author’s home. (Most of the data are real, but some are fabricated.) Each value represents the energy consumed (kWh) in a two-month period. Let each subgroup consist of the six amounts within the same year. Data are available for download at www.TriolaStats.com.
Jan.-Feb. | Mar.-April | May-June | July-Aug. | Sept.-Oct. | Nov.-dec. | |
Year 1 | 3637 | 2888 | 2359 | 3704 | 3432 | 2446 |
Year 2 | 4463 | 2482 | 2762 | 2288 | 2423 | 2483 |
Year 3 | 3375 | 2661 | 2073 | 2579 | 2858 | 2296 |
Year 4 | 2812 | 2433 | 2266 | 3128 | 3286 | 2749 |
Year 5 | 3427 | 578 | 3792 | 3348 | 2937 | 2774 |
Year 6 | 4016 | 3458 | 3395 | 4249 | 4003 | 3118 |
Year 7 | 4016 | 3458 | 3395 | 4249 | 4003 | 3118 |
Year 8 | 4016 | 3458 | 3395 | 4249 | 4003 | 3118 |
Energy Consumption: Run Chart Construct a run chart for the 48 values. Does there appear to be a pattern suggesting that the process is not within statistical control?
Quarters. In Exercises 9–12, refer to the accompanying table of weights (grams) of quarters minted by the U.S. government. This table is available for download at www.TriolaStats.com.
Day | Hour 1 | Hour 2 | Hour 3 | Hour 4 | Hour 5 | \(\bar x\) | s | Range |
1 | 5.543 | 5.698 | 5.605 | 5.653 | 5.668 | 5.6334 | 0.0607 | 0.155 |
2 | 5.585 | 5.692 | 5.771 | 5.718 | 5.72 | 5.6972 | 0.0689 | 0.186 |
3 | 5.752 | 5.636 | 5.66 | 5.68 | 5.565 | 5.6586 | 0.0679 | 0.187 |
4 | 5.697 | 5.613 | 5.575 | 5.615 | 5.646 | 5.6292 | 0.0455 | 0.122 |
5 | 5.63 | 5.77 | 5.713 | 5.649 | 5.65 | 5.6824 | 0.0581 | 0.14 |
6 | 5.807 | 5.647 | 5.756 | 5.677 | 5.761 | 5.7296 | 0.0657 | 0.16 |
7 | 5.686 | 5.691 | 5.715 | 5.748 | 5.688 | 5.7056 | 0.0264 | 0.062 |
8 | 5.681 | 5.699 | 5.767 | 5.736 | 5.752 | 5.727 | 0.0361 | 0.086 |
9 | 5.552 | 5.659 | 5.77 | 5.594 | 5.607 | 5.6364 | 0.0839 | 0.218 |
10 | 5.818 | 5.655 | 5.66 | 5.662 | 5.7 | 5.699 | 0.0689 | 0.163 |
11 | 5.693 | 5.692 | 5.625 | 5.75 | 5.757 | 5.7034 | 0.0535 | 0.132 |
12 | 5.637 | 5.628 | 5.646 | 5.667 | 5.603 | 5.6362 | 0.0235 | 0.064 |
13 | 5.634 | 5.778 | 5.638 | 5.689 | 5.702 | 5.6882 | 0.0586 | 0.144 |
14 | 5.664 | 5.655 | 5.727 | 5.637 | 5.667 | 5.67 | 0.0339 | 0.09 |
15 | 5.664 | 5.695 | 5.677 | 5.689 | 5.757 | 5.6964 | 0.0359 | 0.093 |
16 | 5.707 | 5.89 | 5.598 | 5.724 | 5.635 | 5.7108 | 0.1127 | 0.292 |
17 | 5.697 | 5.593 | 5.78 | 5.745 | 5.47 | 5.657 | 0.126 | 0.31 |
18 | 6.002 | 5.898 | 5.669 | 5.957 | 5.583 | 5.8218 | 0.185 | 0.419 |
19 | 6.017 | 5.613 | 5.596 | 5.534 | 5.795 | 5.711 | 0.1968 | 0.483 |
20 | 5.671 | 6.223 | 5.621 | 5.783 | 5.787 | 5.817 | 0.238 | 0.602 |
Quarters: \(\bar x\)-Chart Treat the 5 measurements from each day as a sample and construct an \(\bar x\)- chart. What does the result suggest?
Quarters. In Exercises 9–12, refer to the accompanying table of weights (grams) of quarters minted by the U.S. government. This table is available for download at www.TriolaStats.com.
Day | Hour 1 | Hour 2 | Hour 3 | Hour 4 | Hour 5 | \(\bar x\) | s | Range |
1 | 5.543 | 5.698 | 5.605 | 5.653 | 5.668 | 5.6334 | 0.0607 | 0.155 |
2 | 5.585 | 5.692 | 5.771 | 5.718 | 5.72 | 5.6972 | 0.0689 | 0.186 |
3 | 5.752 | 5.636 | 5.66 | 5.68 | 5.565 | 5.6586 | 0.0679 | 0.187 |
4 | 5.697 | 5.613 | 5.575 | 5.615 | 5.646 | 5.6292 | 0.0455 | 0.122 |
5 | 5.63 | 5.77 | 5.713 | 5.649 | 5.65 | 5.6824 | 0.0581 | 0.14 |
6 | 5.807 | 5.647 | 5.756 | 5.677 | 5.761 | 5.7296 | 0.0657 | 0.16 |
7 | 5.686 | 5.691 | 5.715 | 5.748 | 5.688 | 5.7056 | 0.0264 | 0.062 |
8 | 5.681 | 5.699 | 5.767 | 5.736 | 5.752 | 5.727 | 0.0361 | 0.086 |
9 | 5.552 | 5.659 | 5.77 | 5.594 | 5.607 | 5.6364 | 0.0839 | 0.218 |
10 | 5.818 | 5.655 | 5.66 | 5.662 | 5.7 | 5.699 | 0.0689 | 0.163 |
11 | 5.693 | 5.692 | 5.625 | 5.75 | 5.757 | 5.7034 | 0.0535 | 0.132 |
12 | 5.637 | 5.628 | 5.646 | 5.667 | 5.603 | 5.6362 | 0.0235 | 0.064 |
13 | 5.634 | 5.778 | 5.638 | 5.689 | 5.702 | 5.6882 | 0.0586 | 0.144 |
14 | 5.664 | 5.655 | 5.727 | 5.637 | 5.667 | 5.67 | 0.0339 | 0.09 |
15 | 5.664 | 5.695 | 5.677 | 5.689 | 5.757 | 5.6964 | 0.0359 | 0.093 |
16 | 5.707 | 5.89 | 5.598 | 5.724 | 5.635 | 5.7108 | 0.1127 | 0.292 |
17 | 5.697 | 5.593 | 5.78 | 5.745 | 5.47 | 5.657 | 0.126 | 0.31 |
18 | 6.002 | 5.898 | 5.669 | 5.957 | 5.583 | 5.8218 | 0.185 | 0.419 |
19 | 6.017 | 5.613 | 5.596 | 5.534 | 5.795 | 5.711 | 0.1968 | 0.483 |
20 | 5.671 | 6.223 | 5.621 | 5.783 | 5.787 | 5.817 | 0.238 | 0.602 |
Quarters: R Chart Treat the five measurements from each day as a sample and construct an R chart. What does the result suggest?
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