Name:
Block:
Math 12 Foundations
Chapter 5 Statistical Reasoning Practice Test (Review)
Multiple Choices: Do not write in this booklet. Record your answers on the answer sheet provided.
1. Environment Canada compiled data on the number of lightning strikes per square kilometre in Alberta and
British Columbia towns from 1999 to 2008.
0.42
0.28
0.13
0.10
0.05
0.04
0.03
0.02
0.00
0.91
0.81
0.70
0.61
0.49
0.42
0.40
0.23
0.12
0.07
0.04
0.03
0.03
0.01
1.08
0.88
Lightning Strikes (per
square kilometer)
0.74
0.66
0.58
0.43
What value goes in the fourth row of this frequency table?
a. 3
b. 5
c. 4
d. 6
0.00–0.19
0.20–0.39
0.40–0.59
0.60–0.79
0.80–0.99
1.00–1.19
Frequency
13
2
6
3
1
2. Which histogram represents the following test scores? Geography Test 4 Scores (our of 100)
98
82
75
66
62
95
81
72
64
58
92
80
72
62
55
85
76
72
62
55
85
75
67
62
41
a.
b.
c.
d.
3. At the end of a bowling tournament, three friends analyzed their scores.
Lada’s mean bowling score is 125 with a standard deviation of 27.
Quinn’s mean bowling score is 182 with a standard deviation of 28.
Kamal’s mean bowling score is 170 with a standard deviation of 20. Who is the more consistent bowler?
a. Impossible to tell.
b. Quinn
c. Kamal
d. Lada
4. A pear orchard has 20 trees with these heights, given in inches.
110
83
104
95
88
80
115
106
97
100
98
93
92
117
75
83
122
115
89
105
Determine the standard deviation, to one decimal place.
a. 9.0 in.
b. 11.0 in
c. 13.0 in
d. 15.0 in
5. A company measured the lifespan of a random sample of 30 light bulbs. Times are in hours.
985 1001 1024 1087
952
910
938
931
1074 1081
1078 1080
982 1108 1022
937
922
1017 1093 1115
880 1048
917 1086
935
936
986
1038 954
966
Determine the mean, to one decimal place.
a. 997.8 h
b. 1012.8 h
c. 1002.8 h
d. 1007.8 h
6. A teacher is analyzing the class results for a physics test. The marks are normally distributed with a mean (µ) of
76 and a standard deviation () of 4. Determine Shondra’s mark if she scored µ + .
a. 80
b. 68
c. 84
7. Which set is normally distributed?
Interval
0–9
10–19
20–29
Set A.
2
5
7
Set B.
5
5
4
Set C.
1
5
9
Set D.
8
9
3
a. Set A.
b. Set B
d. 72
30–39
40–49
50–59
10
5
10
11
15
5
4
8
15
0
1
14
c. Set D
d. Set C
8. Determine the z-score for the given value.
µ = 91.4,  = 3.8, x = 87.6
a. –2
b.
2
c.
–1
d.
1
9. Determine the percent of data to the left of the z-score: z = 1.44.
a. 94.95%
b. 95.91%
c. 93.82%
d. 92.51%
10. Determine the percent of data to the left of the z-score: z = –1.50.
a. 8.08%
b. 6.68%
c.
6.81%
d. 7.35%
11. Determine the percent of data to the left of the z-score: z = 0.87.
a. 80.78%
b. 77.94%
c.
79.71%
d. 78.23%
12. Determine the percent of data to the right of the z-score: z = –1.96.
a. 98.50%
b. 97.50%
c.
1.50%
d. 2.50%
13. Determine the percent of data to the right of the z-score: z = 2.26.
a. 2.12%
b. 2.12%
c. 1.19%
d. 0.91%
14. Determine the percent of data between the following z-scores:
z = –0.45 and z = –0.15.
a. 32.64%
b. 44.04%
c.
76.68%
d. 11.40%
15. A poll was conducted about an upcoming election. The result that 71% of people intend to vote for one of the
candidates is considered accurate within ±3.0 percent points, 9 times out of 10.
State the confidence interval.
a. 69.5%–72.5%
b. 71%–77%
c. 68%–74%
d. 71%–74%
16. The results of a survey have a confidence interval of 28% to 34%, 19 times out of 20.
Determine the margin of error.
a. ±3%
b. ±6%
c. ±5%
d.
±4%
d.
It is impossible to tell.
17. Which sample size will have the least margin of error?
a. 3000
b. 1000
c.
2000
18. In a recent survey of high school students, 72% of those surveyed agreed that school should start half an hour
later. The survey is considered accurate to within 3.5 percent points, 19 times out of 20.
If a high school has 1200 students, state the range of the number of students who would agree with the survey.
a. 864–948
b. 822–906
c. 822–864
d.
864–906
Short Answer
1. An apple orchard has 32 trees with these heights, given in inches.
116
90
91
99
114
110
124
102
82
89
104
102
95
105
118
118
110
97
92
93
91
116
101
101
116
86
101
83
117
93
122
104
If the interval width is 5 and starts at 80, what is the last interval?
2. Determine the z-score for the given value.
µ = 55,  = 1, x = 54.6
3. Determine the percent of data to the left of the z-score: z = 0.71.
.
4. A poll was conducted about an upcoming election. The result that 65% of people intend to vote for one of the
candidates is considered accurate within ±4.2 percent points, 9 times out of 10.
State the confidence interval.
= 60.8 % ~ 69.2 %
.
5. An apple orchard has 32 trees with these heights, given in inches.
116
90
91
99
114
110
124
102
82
89
104
102
95
105
118
118
110
97
92
93
91
116
101
101
116
86
101
83
117
93
132
104
Determine the standard deviation, to one decimal place. (You might not need every row or column of the
table provided
ANS: 12.4 in.
6. Andrea and Raj are trying to control the number of text messages they send. They record the number they
send every day in April.
Andrea: 22, 21, 24, 20, 31, 19, 13, 23, 16, 12, 17, 15, 14, 11, 8, 24, 19, 14, 19, 27, 22, 26, 25, 20, 24, 18, 28, 12, 18, 22
Raj: 12, 8, 9, 3, 2, 12, 33, 28, 32, 28, 29, 13, 16, 14, 30, 26, 31, 32, 32, 13, 16, 26, 18, 32, 26, 9, 10, 2, 8, 16
Create a frequency table for the data. Choose an interval width so you have seven intervals.
ANS: a) The maximum value is 33 and the minimum value is 2, so the range is 31. If the interval width is 5
and starts at 0, then there will be seven intervals and all values are included.
b)
Frequency
Frequency
(Andrea)
(Raj)
Interval
0–4
0
3
5–9
1
4
10–14
6
6
15–19
8
4
20–24
10
1
25–29
4
9
30–34
1
3
7. A tile company produces floor tiles that have an average thickness of 55 mm, with a standard deviation of
0.6 mm. For premium-quality floors, the tiles must have a thickness between 54 mm and 55 mm. What
percent, to the nearest whole number, of the total production can be sold for premium-quality floors?
ANS: Determine the two z-scores:
The z-scores are –1.67 and 0.
.
8. An advertisement for a new toothpaste states that 80% of users reported better dental check-ups. The results
of the poll are accurate within 4 percent points, 9 times out of 10.
a) State the confidence level.
The confidence level is 9 out of 10 or 90%.
b) Determine the confidence interval.
80% + 4% = 84%
80% – 4% = 76%
The confidence interval is 76% to 84%.
c) In a focus group of 41 students, determine the range of the mean number of the students who could expect
better dental check-ups.
50 – 4 – 5 = 41
The number of students trying the toothpaste is 41.
0.76(41) = 31.16
0.84(41) = 34.44
The mean number of students who could expect better dental check-ups should be in
the range of 31 to 34.