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Moraine Valley Community College

MTH 212 – Exam 1

Name: ______________________________________________________________________

This exam is a take home exam. You may use your book, notes, and other resources. You may also work

with others Ã¢â‚¬â€œ however, the final result MUST BE YOUR OWN WORK. Academic dishonesty (including

copying the work of others) will result in failure in the entire course.

List any resources used (other than the textbook or notes) and any people (including tutors) you worked

with below:

Resources Used:

People Worked With:

For multiple choice question or fill in the blank questions, circle the correct answer. You must show your

work where appropriate.

A random sample of ten courses was taken, and the number of students in the courses was determined.

10

32

21

19

11

32

15

18

26

20

Use this data and your calculator (1varstats) to answer questions 1 through 5.

1. The standard deviation of this data set is:

________________________

2. The variance of this data set is:

________________________

3. The median of this data set is:

________________________

4. The first quartile of this data set it:

________________________

5. The mean of this data set is:

________________________

Use the histogram below to answer questions 5-10. If a question canÃ¢â‚¬â„¢t be answered using the graph,

write Ã¢â‚¬Å“cannot be determined from the histogramÃ¢â‚¬Â.

6. The shape of the distribution in the histogram is:

7. How many data points are between 1.5 and 4.5 (including 1.5 but not 4.5)?

8. If the data in the histogram represents a sample, the sample size is:

9. How many times was the value 9 observed in the data set?

10. Approximately what percentage of data values were 7.5 or greater?

Suppose that the mean of a data set is 28 while the standard deviation is 1.4. Use this information to

answer questions 11 and 12.

11. What is the z-score of the data set value 26?

12. Suppose that the z-score for a data value is z = 2.8. What is the data value?

13. At a local community college, five statistics classes are randomly selected out of all the sections

taught and all of the students from three of the courses are interviewed. Identify the sampling

method.

14. The sample standard deviation is represented by (symbol):

15. The population mean is represented by (symbol):

16. Determine if the following variable is quantitative or qualitative(categorical):

The course number of a college class

17. If a distribution is skewed left, then which of the following would best describe the center of the

data set?

a) the mean

b) the standard deviation

c) the median

d) the IQR

18. Determine if the following variable is quantitative or qualitative(categorical):

The number of students taking a course

19. On a factory assembly line, every 100th item is checked for defects. This is an example of what

kind of sampling technique?

20. If a data set has a standard deviation of 15, what is the variance for this data set?

21. Which of the following is an example of cluster sampling?

a) A sample of 100 high school students is randomly chosen to participate in a survey about

study habits.

b) Chosen at random, 25 9th graders, 25 10th graders, 25 11th graders and 25 12th graders are

surveyed about their study habits.

c) A list of all the county high schools is made and 2 are randomly chosen. All students at these

two high schools are surveyed about their study habits.

d) All the high school students living in a 1 mile radius of the school board office are surveyed

regarding their study habits.

22. Suppose a student receives a score on the ACT in the 17th percentile. What percentage of those

taking the ACT scored higher than the student?

23. If a data value has a z-score of zero, that means:

a) It is less than the mean

b) it is equal to the mean

c) it is larger than the mean

d) none of these

24. TRUE OR FALSE: The variance could be negative. Explain why.

25. In a survey conducted by the National Center for Health Statistics, the sample mean height of

women in the United States (aged 20-29) was 64 inches, with a sample standard deviation of

2.71 inches. Estimate the percentage of the women whose heights are between 58.58 inches

and 69.42 inches. (assume the heights follow a bell shaped distribution)

Consider the boxplot below. Use this to answer questions 26 Ã¢â‚¬â€œ 28. If an answer canÃ¢â‚¬â„¢t be determined,

state Ã¢â‚¬Å“cannot be determined from this graph.Ã¢â‚¬Â For numerical values, approximate as best you can using

the gridlines.

26. How many data values are represented?

27. What is the third quartile of this data set?

28. What is the largest observed value?

For the remaining questions, be sure to show your work/ reasoning. Solutions without work or

reasoning may not receive credit.

29. (6 points) Consider the given frequency distribution.

a) Determine the cumulative frequencies and the relative frequencies for each class and add

them to the table.

Class

Frequency

18 to 29

18

29 to 40

20

40 to 51

0

51 to 62

19

Relative Frequency

b) Sketch a histogram to represent the data. Label your axes.

Cumulative Frequency

30. ( 5 points) The distribution of the lengths of bolts has a bell shaped distribution with a mean of 4

inches and a standard deviation of 0.007 inch.

a) About 68% of bolts manufactured will be between what lengths?

b) If the company discards any bolts less than 3.986 inches or greater than 4.014 inches, what

percentage of bolts manufactured will be discarded?

c) What percentage of bolts will be less than 3.979 inches in length?

31. (5 points) Over a year, daily sales at a large store averaged $4,800 with a standard deviation of

$1000. The distribution overall is left skewed.

a) Explain why the empirical rule does not apply to this data set.

b) What is the minimum percentage of days with sales between $2,800 and $6,800?

c) What is the approximate minimum percentage of days with sales between $3300 and

$6300? (HINT: the z score of each number may be helpful.)

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