Foundations 20
Name: ___________________________
Statistical Reasoning Review
Round all answers to 1 decimal place unless otherwise stated.
1. Joel researched the average daily temperature in Lloydminster, SK
Month
Jan. Feb. Mar. Apr. May Jun. Jul Aug
Average -10.0 -17.5 -5.0
3.7
10.7
14.3 20.1 14.0
daily
temp.
(ᵒC)
Determine the mean, median, mode, and range of the data.
2. 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
Complete the frequency table.
Height (in.)
80-89
90-99
100-109
110-119
120-129
130-139
Frequency
Sep. Oct.
9.8
4.8
Nov Dec.
-5.8 -14.8
Foundations 20
Name: ___________________________
3. Why are frequency polygons better for comparing multiple sets of data than histograms?
4. Clair ordered packages of beads from two online companies.
The mean of the masses of the packages from company A is 72 g with a standard deviation of 3.4
g. The mean of the masses of the packages from company B is 68.5 g with a standard deviation of
1.8 g. She ordered 10 packages from each company. Which company’s packages have a more
consistent mass?
5. Three 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 2 136 174 156 176 150 166 142 156 130 182 180 166 148 172
Determine the mean and the standard deviation for each group.
Foundations 20
Question 5 (cont.)
Name: ___________________________
Foundations 20
Name: ___________________________
6. 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
10.0
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.
Foundations 20
Name: ___________________________
7. The ages of members in a hiking club are normally distributed, with a mean of 32 and a standard
deviation of 6 years. What percent of the members are between 26 and 32?
8. The ages of members in a hiking club are normally distributed, with a mean of 32 and a standard
deviation of 6 years. How many members are between 32 and 44 if there are 3000 members?
9. The ages of members in a hiking club are normally distributed, with a mean of 32 and a standard
deviation of 6 years. What percent of the members are younger than 20?
10. The ages of members in a hiking club are normally distributed, with a mean of 32 and a standard
deviation of 6 years. How many members are older than 38 if there are 3000 members?
Foundations 20
Name: ___________________________
11. Determine the z-score for the given value: (round to 2 decimals)
a. 𝑥̅ = 360, σ = 20, x = 315
b. 𝑥̅ = 9.3, σ = 0.4, x = 8.8
c. 𝑥̅ = 5.89, σ = 0.53, x = 5.23
12. A teacher is analyzing the class results for a computer science test. The marks are normally
distributed with a mean of 79.5 and a standard deviation of 3.5. Determine Kaleigh’s mark if her
resulting z-score is 2.5.
13. A teacher is analyzing the class results for a computer science test. The marks are normally
distributed with a mean of 79.5 and a standard deviation of 3.5. Determine Jared’s mark if his
resulting z-score is -2.0.
Foundations 20
Name: ___________________________
For questions 14 – 22, round answers to 2 decimal places.
14. Determine the percent of data to the left of the z-score: z = 1.05
15. Determine the percent of data to the left of the z-score: z = -2.20
16. Determine the percent of data to the left of the z-score: z = 0.71
17. Determine the percent of data to the right of the z-score: z = -0.19
18. Determine the percent of data to the right of the z-score: z = -0.68
19. Determine the percent of data to the right of the z-score: z = 1.60
Foundations 20
Name: ___________________________
20. Determine the percent of data between the following z-scores: z = -0.14 and z = 1.74
21. Determine the percent of data between the following z-scores: z = 0.34 and z = 1.70
22. Determine the percent of data between the following z-scores: z = -2.99 and z = 1.50
23. A poll was conducted about an upcoming election. The results are considered accurate within
+4.0 percent points, 9 times out of 10. State the confidence level.
24. The results of a survey have a confidence interval of 29%to 37%, 9 times out of 10. Determine
the margin of error.
Foundations 20
Name: ___________________________
25. A poll was conducted about an upcoming election. The result that 18% of people intend to vote
for one of the candidates is considered accurate within +4.5 percent points, 9 times out of 10.
State the confidence level.
26. The results of a survey have a confidence interval of 74.9% to 79.1%, 9 times out of 10.
Determine the margin of error.
27. 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.
Interpret the data.
28. Jackson raises Siberian husky sled dogs at his kennel. He knows, from the data he has collected
over the years, that the masses of adult male dogs are normally distributed, with a mean of 23.6
kg and a standard deviation of 1.8 kg.
a. How many of his 87 adult male dogs would you expected to be in the range 21.8 kg to 25.4
kg to the nearest whole dog.
Foundations 20
Name: ___________________________
b. Jackson has 48 male puppies this year. How many of them could he expect to have a mass
greater than 20 kg when they grow up (to the nearest whole dog)?
Foundations 20
Name: ___________________________
Answers:
1. Mean = 2.0ᵒC
2.
Median = 4.3ᵒC
Height (in.)
80-89
90-99
100-109
110-119
120-129
130-139
Mode = None
Range = 37.6ᵒC
Frequency
4
9
8
9
1
1
3. You can compare all the data on one graph and it is clearer to see the relationship/difference in
values from each set of data.
4. Company B will since is has a lower standard deviation.
5. Group 1: Mean = 147.6 Standard Deviation = 23.4
Group 2: Mean = 159.6 Standard Deviation = 16.1
6. Standard Deviation 0.95 h
7. 34%
8. 1425
9. 2.5%
10. 480
11. a. -2.25
12. 88.3%
13. 72.5%
14. 85.31%
15. 1.39%
16. 76.11%
17. 57.53%
18. 75.17%
b. -1.25
c. -1.25
Foundations 20
Name: ___________________________
19. 5.48%
20. 51.48%
21. 32.23%
22. 93.18%
23. 90%
24. +4 percent points
25. 13.5 to 22.5%
26. +2.1
27. With 90% confidence, it can be said that 60.8% to 69.2% of people intend to vote for one of the
candidates.
28. 59 dogs
29. 47 male puppies