Review Questions
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C HAPTER
Chapter 1. Review Questions
1
Review Questions
Part A. For each question, circle the most appropriate answer. 1. If the standard deviation of a population is 6, the population variance is: a. b. c. d.
2.44 3 6 36
2. What is the population standard deviation of the following data values? 3.3 a. b. c. d.
2.9
8.5
11.5
3.61 4.17 6.55 13.52
3. Suppose data are normally distributed, with a mean of 100 and a standard deviation of 20. Between what 2 values will approximately 68% of the data fall? a. b. c. d.
60 and 140 80 and 120 20 and 100 100 and 125
4. The sum of all of the deviations about the mean of a set of data is always going to be equal to: a. b. c. d.
positive the mode the standard deviation total 0
5. What is the population variance of the following data values? 40 a. b. c. d.
38
42
47
35
4.03 4.51 16.24 20.34
6. Suppose data are normally distributed, with a mean of 50 and a standard deviation of 10. Between what 2 values will approximately 95% of the data fall? a. b. c. d.
40 and 60 30 and 70 20 and 80 10 and 95 1
www.ck12.org 7. Suppose data are normally distributed, with a mean of 50 and a standard deviation of 10. What would be the variance? a. b. c. d.
10 40 50 100
8. If data are normally distributed, what percentage of the data should lie within the range of µ ± 3σ? a. b. c. d.
34% 68% 95% 99.7%
9. If a normally distributed population has a mean of 75 and a standard deviation of 15, what proportion of the values would be expected to lie between 45 and 105? a. b. c. d.
34% 68% 95% 99.7%
10. If a normally distributed population has a mean of 25 and a standard deviation of 5.5, what proportion of the values would be expected to lie between 19.5 and 30.5? a. b. c. d.
34% 68% 95% 99.7%
Part B. Answer the following questions and show all work (including diagrams) to create a complete answer.
11. In the United States, cola can normally be bought in 8 oz cans. A survey was conducted where 250 cans of cola were taken from a manufacturing warehouse and the volumes were measured. It was found that the mean volume was 7.5 oz, and the standard deviation was 0.1 oz. Draw a normal distribution curve to represent this data and then answer the following questions. (a) 68% of the volumes can be found between __________ and _________. (b) 95% of the volumes can be found between __________ and _________. (c) 99.7% of the volumes can be found between __________ and _________. 12. The mean height of the fourth graders in a local elementary school was found to be 4’8”, or 56”. The standard deviation was found to be 5”. Draw a normal distribution curve to represent this data and then answer the 2
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Chapter 1. Review Questions
following questions. (a) 68% of the heights can be found between __________ and _________. (b) 95% of the heights can be found between __________ and _________. (c) 99.7% of the heights can be found between __________ and _________. 13. The following data was collected: 5 8 9 10 4 3 7 5 Fill in the chart below and calculate the standard deviation and the variance.
TABLE 1.1: Data (x)
Mean (µ)
Data − Mean (x − µ)
Square of Data − Mean (x − µ)2
∑ 14. The following data was collected. 11 15 16 12 19 17 in the chart below and calculate the standard deviation and the variance.
14
18
15
10 Fill
TABLE 1.2: Data (x)
Mean (µ)
Data − Mean (x − µ)
Square of Data − Mean (x − µ)2
∑
15. Mrs. Meery has recorded her exam results for the current mathematics exam. The results are shown below: 3
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64
98
78
76
56
48
89
78
69
90
89
97
67
58
59
50
78
89
68
83
72
91
(a) Determine the mean for this data. (b) Determine the standard deviation for this data. (c) Determine the variance for this data. (d) Draw a normal distribution curve to represent the data Mrs. Meery found in her class. 16. Mrs. Landry decided to do the same analysis as Mrs. Meery for her math class. She has recorded her exam results for the current mathematics exam. The results are shown below: 89
87
81
84
76
72
67
49
55
38
67
90
59
87
89
69
92
90
79
84
69
93
85
70
87
80
(a) Determine the mean for this data. (b) Determine the standard deviation for this data. (c) Determine the variance for this data. (d) Draw a normal distribution curve to represent the data Mrs. Landry found in her class. 17. 200 senior high students were asked how long they had to wait in the cafeteria line for lunch. Their responses were found to be normally distributed, with a mean of 15 minutes and a standard deviation of 3.5 minutes. Copy the following bell curve onto your paper and answer the questions below.
(a) How many students would you expect to wait more than 11.5 minutes? (b) How many students would you expect to wait more than 18.5 minutes? (c) How many students would you expect to wait between 11.5 and 18.5 minutes? 18. 350 babies were born at Neo Hospital in the past 6 months. The average weight for the babies was found to be 6.8 lbs, with a standard deviation of 0.5 lbs. Copy the following bell curve onto your paper and answer the questions below. 4
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Chapter 1. Review Questions
(a) How many babies would you expect to weigh more than 7.3 lbs? (b) How many babies would you expect to weigh more than 7.8 lbs? (c) How many babies would you expect to weigh between 6.3 and 7.8 lbs? 19. Sudoku is a very popular logic game of number combinations. It originated in the late 1800’s by the French press, Le Siècle. The average times (in minutes) it takes those in a senior math class to complete a Sudoku puzzle are found below. Draw a normal distribution curve to represent this data. Determine what time a student must complete a Sudoku puzzle in to be in the top 0.13%.
20
15
21
24
7
19
10
17
15
22
31
19
20
21
21
9
12
26
24
28
19
16
24
11
17
31
25
13
16
18
22
32
9
15
19
27
14
25
32
29
20. Sheldon has planted seedlings in his garden in the back yard. After 30 days, he measures the heights of the seedlings to determine how much they have grown. The differences in heights can be seen in the table below. The heights are measured in inches. Draw a normal distribution curve to represent the data. Determine what the range of the differences in heights of the seedlings is for the middle 68% of the data.
10
3
8
4
7
12
8
5
4
6
10
7
10
11
8
12
9
10
9 7
3
8
8
11
5
