Question

MATH399 Applied Managerial Statistics

Week 1 Assignment Skewness and Standard Deviation

QuestionBased on the z-scores calculated above for Stephan’s
electric bills in IL and FL, in which city is his electric bill
higher, when compared to their respective distributions?

Illinois

Florida

Stephan’s electric bills in both states are comparable.

There is not enough information for a comparison.

QuestionWhen Stephan moved from Illinois to Florida, his
average monthly electric bill increased from $83 to $102. He
is curious to know whether his IL or FL electric bill is relatively
more or less expensive, when compared to the distribution of
electric bills for each state. In Illinois, the mean monthly
electric bill is $85, with a standard deviation of $3.20. In
Florida, the mean monthly electric bill is $105, with a standard
deviation of $4.00.

Compute the z-scores for Stephan’s IL and FL electric bills.
Round to three decimal places if necessary.

QuestionBased on the z scores found above, on which college
entrance exam did Seam perform better, compared to the national
distributions for each test?

QuestionNational results for the SAT test show that for
college-bound seniors the average combined SAT Writing, Math and
Verbal score is 1500 with a standard deviation of 250. National
results for the ACT test show that for college-bound seniors the
average composite ACT score is 20.4 with a standard deviation of
4.8.

Sean took both the SAT and the ACT college entrance
exams. His SAT score was 1700 and his ACT score was 24.
He wants to know on which test he performed better.

Find the z-scores for his result on each exam.

QuestionA math class’s mean test score is 88.4. The standard
deviation is 4.0. If Kimmie scored 85.9, what is her z-score?

−1.6

−0.625

0.625

1.6

Using Z-Scores to Compare Data

Key Terms

•
Z-score: a measure of how far a point is from the mean, measured in
standard deviations, denoted by the letter z

Z-score is also referred to as the Test statistic

QuestionBased on the z scores found above, is Kathy or Linda’s
starting salary higher, when compared to the salary distributions
of each company?_

QuestionKathy and Linda both accepted new jobs at different
companies. Kathy’s starting salary is $31,500and Linda’s starting
salary is $33,000. They are curious to know who has the better
starting salary, when compared to the salary distributions of their
new employers.

A website that collects salary information from a sample of
employees for a number of major employers reports that
Kathy’s company offers a mean salary of $42,000 with a standard
deviation of $7,000. Linda’s company offers a mean salary of
$45,000 with a standard deviation of $6,000.

Find the z-scores corresponding to each woman’s
starting salary.

QuestionThe following data values represent the daily amount
spent by a family each day during a 7 day summer vacation.

Find the standard deviation of this data set:

$96,$125,$80,$110,$75,$100,$121

Round the final answer to one decimal place.

QuestionThe following data values represent the daily amount
spent by a family each day during a 7 day summer vacation.

Find the variance of this dataset:

$96,$125,$80,$110,$75,$100,$121

•
Round the final answer to one decimal place.

QuestionThe following data values represent the daily amount
spent by a family each day during a 7 day summer vacation.

$96,$125,$80,$110,$75,$100,$121

To determine the “spread” of the data, would you employ
calculations for the sample standard deviation, or population
standard deviation for this data set?

Use calculations for sample standard deviation

Use calculations for population standard deviation

QuestionA food processing plant fills snack-sized bags of
crackers. The mean number of crackers in each bag is 22 and the
standard deviation is 2. The factory supervisor selects one bag
that contains 24 crackers.

Which of the following statements is true?

The number of crackers in the supervisor’s bag is 2 standard
deviations to the right of the mean.

The number of crackers in the supervisor’s bag is 2
standard deviations to the left of the mean.

The number of crackers in the supervisor’s bag is 1
standard deviation to the right of the mean.

The number of crackers in the supervisor’s bag is 1
standard deviation to the left of the mean.

QuestionWhich of the following frequency tables show a skewed
data set? Select all answers that apply.

•

Value Frequency

0
2

1
11

2
30

3
22

4
15

5
12

6
6

7
1

8
1

•
________________________________________

•

Value Frequency

4
1

5
2

6
3

7
7

8
19

9
17

10
17

11
15

12
12

13
4

14
1

15
2

•
________________________________________

•

Value Frequency

13
1

14
6

15
9

16
15

17
27

18
28

19
10

20
4

•
________________________________________

•

Value Frequency

3
1

4
0

5
1

6
5

7
9

8
12

9
12

10
18

11
12

12
17

13
11

14
0

15
1

16
0

17
1

QuestionWhich of the data sets represented by the following
histograms has the largest standard deviation?

A histogram has a horizontal axis from 0.00 to 50.00 in
increments of 2.00 and a vertical axis from 0 to 100 in increments
of 25. The histogram has vertical bars of width 2.00 starting at
the horizontal axis value 22.00. The approximate heights of the
bars are as follows, where the left horizontal axis label is listed
first and the approximate height is listed second: 14.00, 80;
16.00, 95; 18.00, 45.

A histogram has a horizontal axis from 0.00 to 50.00 in
increments of 2.00 and a vertical axis from 0 to 100 in increments
of 25. The histogram has vertical bars of width 2.00 starting at
the horizontal axis value 12.00. The approximate heights of the
bars are as follows, where the left horizontal axis label is listed
first and the approximate height is listed second: 12.00, 67;
14.00, 80; 16.00, 95; 18.00, 75; 20.00, 75.

A histogram has a horizontal axis from 0.00 to 50.00 in
increments of 2.00 and a vertical axis from 0 to 100 in increments
of 25. The histogram has vertical bars of width 2.00 starting at
the horizontal axis value 18.00. The approximate heights of the
bars are as follows, where the left horizontal axis label is listed
first and the approximate height is listed second: 18.00, 50;
20.00, 70; 22.00, 74; 24.00, 78; 26.00, 83; 28.00, 81; 30.00, 80;
32.00, 74; 34.00, 60.

A histogram has a horizontal axis from 0.00 to 50.00 in
increments of 2.00 and a vertical axis from 0 to 100 in increments
of 25. The histogram has vertical bars of width 2.00 starting at
the horizontal axis value 8.00. The approximate heights of the bars
are as follows, where the left horizontal axis label is listed
first and the approximate height is listed second: 8.00, 49; 10.00,
51; 12.00, 51; 14.00, 53; 16.00, 51; 18.00, 51; 20.00, 48; 22.00,
49; 24.00, 51; 26.00, 53; 28.00, 50; 30.00, 53; 32.00, 51; 34.00,
53; 36.00, 52; 38.00, 46.

QuestionIf the mean of a data set is 32 and the median is 36,
which of the following is most likely?

The data are skewed to the left.

The data are skewed to the right.

The data are symmetric.

QuestionWhich of the following box-and-whisker plots shows a
skewed data set? Select all answers that apply.

A horizontal box-and-whisker plot is above a horizontal axis
labeled from 0 to 18 in increments of 2. The box-and-whisker plot
has the following five-number summary: 2, 8, 9, 10, and 16. All
values are approximate. The part of the box at point 9 is
represented with a dotted line.

A horizontal box-and-whisker plot is above a horizontal axis
labeled from 0 to 20 in increments of 5. The box-and-whisker plot
has the following five-number summary: 3, 9, 10, 11, and 18. All
values are approximate. The part of the box at point 10 is
represented with a dotted line.

A horizontal box-and-whisker plot is above a horizontal axis
labeled from 0 to 16 in increments of 2. The box-and-whisker plot
has the following five-number summary: 1, 3, 4, 6, and 15. All
values are approximate. The part of the box at point 4 is
represented with a dotted line.

A horizontal box-and-whisker plot is above a horizontal axis
labeled from 0 to 20 in increments of 5. The box-and-whisker plot
has the following five-number summary: 4, 14, 16, 19, and 20. All
values are approximate. The part of the box at point 16 is
represented with a dotted line.

QuestionWhich of the data sets represented by the following
histograms has the largest standard deviation?

A histogram has a horizontal axis from 0.00 to 90.00 in
increments of 10.00 and a vertical axis from 0 to 100 in increments
of 25. The histogram has vertical bars of width 10.00 starting at
the horizontal axis value 30.00. The approximate heights of the
bars are as follows, where the left horizontal axis label is listed
first and the approximate height is listed second: 30.00, 51;
40.00, 60; 50.00, 87; 60.00, 71.

A histogram has a horizontal axis from 0.00 to 90.00 in
increments of 10.00 and a vertical axis from 0 to 100 in increments
of 25. The histogram has vertical bars of width 10.00 starting at
the horizontal axis value 30.00. The approximate heights of the
bars are as follows, where the left horizontal axis label is listed
first and the approximate height is listed second: 30.00, 31;
40.00, 42; 50.00, 48; 60.00, 34; 70.00, 25.

A histogram has a horizontal axis from 0.00 to 90.00 in
increments of 10.00 and a vertical axis from 0 to 100 in increments
of 25. The histogram has vertical bars of width 10.00 starting at
the horizontal axis value 40.00. The approximate heights of the
bars are as follows, where the left horizontal axis label is listed
first and the approximate height is listed second: 40.00, 82;
50.00, 76; 60.00, 70; 70.00, 98; 80.00, 76.

A histogram has a horizontal axis from 0.00 to 90.00 in
increments of 10.00 and a vertical axis from 0 to 100 in increments
of 25. The histogram has vertical bars of width 10.00 starting at
the horizontal axis value 0.00. The approximate heights of the bars
are as follows, where the left horizontal axis label is listed
first and the approximate height is listed second: 0.00, 55; 10.00,
32; 20.00, 34; 30.00, 50; 40.00, 61; 50.00, 87; 60.00, 70; 70.00,
62; 80.00, 46; 90.00, 48.

QuestionBased on the z-scores calculated above for Martin and
Lawrence, whose salary is higher, when compared to their companies?

Martin

Lawrence

Neither salary is higher, when compared to the company
salaries.

There is not enough information for a comparison.

QuestionMartin and Lawrence want to know whose salary is
higher, when compared to the distribution of salaries at their
jobs. The table shows their salaries, as well as the mean salary
and standard deviation for each of the companies at which they
work.

Name Annual Salary
Company

Mean Salary Company

Standard Deviation

Martin $44,000 $40,000 $6,400

Lawrence
$46,000 $41,500 $7,200

Find the z-scores corresponding to each man’s salary. Round
to three decimal places, if necessary.

QuestionUsing the following set of data (the same as in the
previous problem), find the population standard deviation: 8, 9, 5,
12, 6.

The population variance of this data set is 6.

QuestionFind the population variance of the following set of
data:

8, 9, 5, 12, 6.

QuestionA group of five friends are long-distance runners who
will be running in an upcoming marathon. To prepare for the
marathon, each of the friends recorded the number of miles they ran
each week for 12weeks. The results of the friends’ training are
shown in the data set provided below. Which of the friends was the
most consistent with the number of miles run each week during the
training? Hint: You should not need to compute the standard
deviation for each friend.

Ashton

Caleb

Jordan

Kyle

Noah

24

35

22

15

13

34

36

39

26

29

25

34

26

24

18

31

35

41

25

31

19

37

38

27

15

33

35

37

24

19

27

34

40

25

27

29

36

27

26

32

36

35

21

32

15

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Ashton

Caleb

Jordan

Kyle

Noah

QuestionYou are told that a data set has a median of 64 and a
mean of 52. Which of the following is a logical conclusion?

The data are skewed to the left.

The data are skewed to the right.

The data are symmetric.

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