Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Environment Canada recorded the amount of rain (in millimetres) in Victoria, BC
for two months. 0 0
9.0 0 0
1.0 0 0
0 7.6 0
0 5.8
0.6 0 0
0.4 0 0
0 0 0 0
0 0 0 0
0 0 0
0 0 0 0
0 0 0
0.4 0 5.8
0 0 1.6
0.2 0 6.0
0 0 0.2
0 0 0.2
0 0 1.0
0 0 2.8
0 0 26.0
0 What value goes in the third row of this frequency table? Precipitation (mm) |
Frequency
| 0–4.9 | 56 | 5.0–9.9 | 5 | 10.0–14.9 | | 15.0–19.9 | 0 | 20.0–24.9 | 0 | 25.0–29.9 | 1 | | |
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2.
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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 0.04
0.81 0.40
0.03 0.74
0.28
0.03 0.70
0.23 0.03
0.66
0.13 0.02
0.61 0.12
0.01 0.58
0.10
0.00 0.49
0.07 1.08
0.43
0.05 0.91
0.42 0.04 0.88
Determine the mean,
to two decimal places.
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3.
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Chinedu recorded the time it takes him to get to school using three different
routes. | Hour | 1 | 2 | 3 | 4 | 5 | | Route 1 (min) | 13 | 15 | 12 | 12 | 16 | | Route 2 (min) | 20 | 18 | 20 | 12 | 17 | | Route 3 (min) | 16 | 17 | 15 | 17 | 22 | | | | | | |
On which route does
Chinedu have a more consistent travel time?
a. | Route 1 | b. | Route 2 | c. | Route
3 |
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4.
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Which description does not describe the normal curve?
a. | shaped like a bell | b. | starts off increasing | c. | symmetrical | d. | always
increasing |
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5.
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The ages of participants in a bonspiel are normally distributed, with a mean of
40 and a standard deviation of 10 years. What percent of the curlers are between 20 and
30?
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6.
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The ages of participants in a bonspiel are normally distributed, with a mean of
40 and a standard deviation of 10 years. What percent of the curlers are between 30 and
50?
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7.
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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 (s) of 4.
Determine Olivia’s mark if she scored µ – s.
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8.
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Determine the z-score for the given value.
µ = 52, s = 6, x = 64
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9.
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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% |
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10.
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Determine the percent of data to the right of the z-score: z =
2.26.
a. | 2.12% | b. | 1.58% | c. | 1.19% | d. | 0.91% |
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11.
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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% |
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12.
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Determine the percent of data between the following z-scores:
z
= 0.40 and z = 1.80.
a. | 30.87% | b. | 22.66% | c. | 15.44% | d. | 7.72% |
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13.
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Determine the percent of data between the following z-scores:
z
= –2.25 and z = 1.75.
a. | 95.99% | b. | 94.77% | c. | 93.55% | d. | 97.23% |
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14.
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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. | 74%–77% | d. | 71%–74% |
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15.
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In a recent survey of high school students, one third of those surveyed said
they would vote for Melissa as student council treasurer. The survey is considered accurate to within
5 percent points, 19 times out of 20.
If a high school has 1200 students, state the range of the
number of votes Melissa should expect.
a. | 340–460 | b. | 300–500 | c. | 200–600 | d. | 370–430 |
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Short Answer
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16.
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Four groups of students recorded their pulse rates after a 2 km run. | Group
1 | 126 | 168 | 158 | 192 | 146 | 166 | 104 | 164 | 116 | 138 | 172 | 136 | 152 | 128 | | Group 2 | 158 | 132 | 156 | 160 | 108 | 150 | 178 | 136 | 172 | 140 | 126 | 154 | 130 | 160 | | Group 3 | 136 | 174 | 156 | 176 | 150 | 166 | 142 | 156 | 130 | 182 | 180 | 166 | 148 | 172 | | Group 4 | 144 | 150 | 142 | 152 | 174 | 176 | 118 | 152 | 178 | 164 | 128 | 158 | 158 | 166 | | | | | | | | | | | | | | | |
Determine the standard deviation of Group 3, to one decimal
place.
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17.
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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.
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18.
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A company measured the lifespan of a random sample of 20 batteries in their MP3
players. Times are in hours.
7.8
11.0 10.5
8.8 9.0 9.4
10.2 9.4
8.6 9.0
9.3 8.5 7.9
9.1 7.9 9.3
7.4 9.7
10.6 8.5
Determine the standard deviation, to two decimal
places.
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Problem
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19.
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The result of all the rolls in a game using four dice are recorded. Sum | Frequency | 4–6 | 5 | 7–9 | 13 | 10–12 | 31 | 13–15 | 35 | 16–18 | 29 | 19–21 | 11 | 22–24 | 2 | | |
a) Graph the data. Does the data appear
to have a normal distribution? b) Determine the mean and standard deviation of the data. Do
these values validate your answer to part a)?
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20.
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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.
b) Determine the confidence interval.
c)
In a focus group of 50 students, four said they already used this toothpaste and another five did
not want to try it. Determine the range of the mean number of the remaining students who could expect
better dental check-ups.
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21.
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Two different market research companies conducted a survey on the same issue.
Company A used a 90% confidence level and company B used a 95% confidence level.
a) If both
companies used the same sample size, what does this imply about the margin of error for each
survey?
b) If both companies used the same margin of error of ±3.5%, what does this
imply about the sample size for each survey?
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