Contemporary Mathematics

# Chapter 8

8.1
1.
None of the above (there’s no sample being selected here; the entire population is being surveyed)
2.
Stratified random sample (the strata are the different majors)
3.
Simple random sample
8.2
1.

Major Frequency
Biology 6
Education 1
Political Science 3
Sociology 2
Undecided 4
8.3
1.

Number of people in the residence Frequency
1 12
2 13
3 8
4 6
5 1
8.4
1.

Age range Frequency
25-29 2
30-34 6
35-39 2
40-44 4
45-49 1
50-54 2
55-59 2
60-64 0
65-70 1

(Answers may vary depending on bin boundary decisions)

8.5
1.
Major Frequency Proportion
Biology 6 37.5%
Education 1 6.3%
Political Science 3 18.8%
Sociology 2 12.5%
Undecided 4 25%
Note that these percentages add up to 100.1%, due to the rounding.
8.6
1.
8.7
1.
Southeast
2.
Just over 10%
3.
Outlying Areas and Rocky Mtns.
8.8
1.
8.9
1.
Twenty-four
2.
The longest commutes are 60, 50, and 36 miles; the shortest are 4, 6, and 7 miles.
3.
4, 6, 7, 10, 10, 10, 12, 12, 12, 14, 15, 18, 18, 20, 25, 25, 25, 30, 30, 35, 35, 36, 50, 60
8.10
1.

 4 7 5 9 7 4 6 9 8 7 7 8 7 5 2 2 1 0 8 9 6 5 4 4 1 9 7 7 6 3 3 1 10 7 6 3 1
8.11
1.
8.12
1.

Answers may vary based on bin choices. Here’s the result for bins of width 2,500:

The data are strongly right-skewed.

8.13
1.
8.14
1.

Top ten teams by wins:

8.15
1.
There are two modes: 89 and 104, each of which appears three times.
8.16
1.

2

8.17
1.
136
8.18
1.
82.5
8.19
1.
2
8.20
1.
12.556
8.21
1.
$\frac{{62}}{{33}} = 1.879$
8.22
1.
Modes: 72, 84, 93, 97
Median: 82.5
Mean: 80.967 (rounded to three decimal places)
8.23
1.
Mode or median
2.
Median or mean
3.
Median or mean
8.24
1.
67
8.25
1.
$\ 74,514 - \ 480 = \ 74,034$
8.26
1.

$s = \sqrt {752.5} \approx 27.432$

8.27
1.
$13,333.77. 8.28 1. 15 2. 70th percentile 8.29 1. 1026 2. 1318 3. 82.7th 4. 99.2nd 8.30 1.$3,120
2.
$26,465.20 3. 32.3rd 4. 98.5th 8.31 1. The red (leftmost) distribution has mean 11, the blue (middle) has mean 13, and the yellow (rightmost) has mean 14. 8.32 1. 6 8.33 1. Mean: 150; standard deviation: 20 8.34 1. 99.7% 2. 95% 3. 68% 8.35 1. 65 and 75 2. 26 and 54 3. 110 and 290 8.36 1. 47.5% 2. 15.85% 3. 81.5% 8.37 1. $−1.8$ $1.6$ $−0.6$ 8.38 1. –44 30 6 8.39 1. 80th 9th 97th 8.40 1. 3.9 6.3 2.9 8.41 1. 1.29 2. 94.5th 3. An LSAT score of 161 is better 8.42 1. 72 2. 6 3. 93rd 8.43 1. Using NORM.INV: 1092.8 Using PERCENTILE: 1085 8.44 1. Income 2. Either; neither one seems to directly influence the other (they’re both influenced by the student’s academic ability) 3. GPA 8.45 1. 8.46 1. 8.47 1. $\,$ 1. No curved pattern 2. Strong negative relationship, $r \approx - 0.9$ 2. $\,$ 1. Curved pattern 3. $\,$ 1. No curved pattern 2. No apparent relationship, $r \approx 0$ 4. $\,$ 1. No curved pattern 2. Weak positive relationship, $r \approx 0.6$ 8.48 1. 1. $r = - 0.91$ 2. Not appropriate 3. $r = - 0.01$ 4. $r = 0.62$ 8.49 1. $y = 0.75\left( \frac{20}{5} \right)(x - 100) + 200 = 3x - 100$ 8.50 1. $y = 1.8x + 16.9$ 8.51 1. $y = 0.174x + 14.5$ 2. 26.68 3. Predicted: 28; actual: 18. The Phillies were caught around 10 fewer times than expected. 4. Every 10 additional steal attempts will result in getting caught about 1.7 times on average. 8.52 1. $y = 0.5481x + 0.1055$, where x is the proportion of made field goals and y is the proportion of made three-point field goals 2. 0.347 3. Predicted: 0.340; actual: 0.368. The Aces made about 2.8% more of their three-point shots than expected. 4. An increase of 1% in made field goal attempts will result in an expected increase of 0.55% in made three-point field goal attempts. ### Check Your Understanding 1. Randomization is being used; cluster random sample. 2. No randomization is being used. 3. Randomization is being used; stratified random sample. 4. Genre Frequency Cooking 1 Non-fiction 3 Romance 4 Thriller 3 True Crime 3 Young Adult 6 5. Number of classes Frequency 1 1 2 3 3 16 4 8 5 4 6. Range of Cell Phone Subscriptions Per Hundred People Frequency 0.0 – 24.9 1 25.0 – 49.9 3 50.0 – 74.9 1 75.0 – 99.9 6 100.0 – 124.9 7 125.0 – 149.9 3 150.0 – 174.9 3 175.0 – 199.9 1 (Note: Answers may vary based on choices made about bins.) 7. 8. 9.  12 7 13 0 2 3 6 6 7 8 9 9 14 1 2 3 3 6 8 8 15 3 3 5 6 6 6 7 7 8 8 16 4 7 8 10. 11. (data source:https://data.ed.gov/) 12. (data source: https://data.ed.gov/) (data source: https://data.ed.gov/) 13. Mode: 112 Median: 113 Mean: 112.64 14. 3 15. 3 16. $\frac{107}{32} \approx 3.344$ 17. 156 18. 147 19. 147.2 20. Mode: not useful; every value appears only once Median: 0.322 Mean: 0.3612 21. Mode: not useful; every value appears only once Median:$42,952

Mean: $42924.78 22. Mode:$13,380
Median: $11,207 Mean:$15,476.79
23.
Since the data are right skewed, the mean will be bigger than the mean. Thus, the workers would rather use the median, while the management will prefer the mean.
24.
9
25.
$\sqrt {10.5} \approx 3.240$
26.
$168 - 127 = 41$
27.
11.306
28.
Range: $0.6617 - 0.1404 = 0.5213$
29.
Standard deviation: 0.170
30.
Range: $\ 43,394 - 42,218 = \ 1,176$
31.
Standard deviation: $398.37 32. 18 33. 14 34. 80th 35. 60th 36. 71.7 37. 101.2 38. 70.25 39. 51.7th 40. 79.3rd 41. 13.8th 42. 95% 43. 34% 44. 84th 45. 0.583 46. 71.2 47. 72nd 48. 115.38 49. 27th 50. 23.2 51. 1300 on the SAT 52. $\mu = 60$; $\sigma = \frac{1}{2}\sqrt {120} \approx 5.477$ 53. 96.6th 54. 57 55. PERCENTILE gives 20.86; NORM.INV gives 21.11. 56. PERCENTILE gives 11.82; NORM.INV gives 11.68. 57. PERCENTRANK gives 92.6th; NORM.DIST gives 91.9th. 58. PERCENTRANK gives 77th; NORM.DIST gives 79.2nd. 59. 60. 1. Yes 61. 1. No 2. Weak positive relationship; $r \approx 0.5$ 62. 0.96 63. $y = 2900 x\, –\, 478$ 64.$7,475

65.

Less than expected by $1,495.68 66. For every$1,000 increase in out-of-state tuition, we expect average monthly salary to increase by \$161.

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