Test 3
Version A KEY
MATH 1010
Essential Mathematics
Fall 2015
Sections 6A – 7C
Formulas
Mean = x =
sum of all values
total number of values
Range = highest value – lowest value
Standard Deviation =
sum of (deviations from the mean)2
total number of data values − 1
68-95-99.7 Rule
z = standard score =
z-score
-3.5
-3.0
-2.9
-2.8
-2.7
-2.6
-2.5
-2.4
-2.3
-2.2
-2.1
-2.0
-1.9
-1.8
-1.7
-1.6
-1.5
-1.4
-1.3
-1.2
-1.1
Percentile
.02
.13
.19
.26
.35
.47
.62
.82
1.07
1.39
1.79
2.28
2.87
3.59
4.46
5.48
6.68
8.08
9.68
11.51
13.57
data value − mean x − µ
=
standard deviation
σ
z-score
-1.0
-.95
-.90
-.85
-.80
-.75
-.70
-.65
-.60
-.55
-.50
-.45
-.40
-.35
-.30
-.25
-.20
-.15
-.10
-.05
0.0
Percentile
15.87
17.11
18.41
19.77
21.19
22.66
24.20
25.78
27.43
29.12
30.85
32.64
34.46
36.32
38.21
40.13
42.07
44.04
46.02
48.01
50.00
z-score
0.0
.05
.10
.15
.20
.25
.30
.35
.40
.45
.50
.55
.60
.65
.70
.75
.80
.85
.90
.95
1.0
Percentile
50.00
51.99
53.98
55.96
57.93
59.87
61.79
63.68
65.54
67.36
69.15
70.88
72.57
74.22
75.80
77.34
78.81
80.23
81.59
82.89
84.13
z-score
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.0
3.5
Percentile
86.43
88.49
90.32
91.92
93.32
94.52
95.54
96.41
97.13
97.72
98.21
98.61
98.93
99.18
99.38
99.53
99.65
99.74
99.81
99.87
99.98
Version A KEY – Page 1 of 17
Test 3
Version A KEY
MATH 1010
Essential Mathematics
P(A) =
Fall 2015
Sections 6A – 7C
number of ways A can occur
total number of possible outcomes
P(A) + P(not A) = 1
P(not A) = 1 – P(A)
P(A and B) = P(A) × P(B)
P(A and B) = P(A) × P(B given A)
P(A or B) = P(A) + P(B)
P(A or B) = P(A) + P(B) – P(A and B)
P(A at least once) + P(A zero times) = 1
P(A happens at least once in n trials) = 1 – P(A happens zero times in n trials)
= 1 – [P(A happens zero times in one trial)]
n
 value of   probability   value of   probability 
Expected Value =  st
×
 +  nd
×
 + …
st
nd
1
event
of
1
event
2
event
of
2
event

 
 
 

Standard Deck of Cards
Colors Suits
Black
Clubs
Spades
Red
Hearts
Diamonds
2
3
Number Cards
4
5
6
7
8
9
Face Cards
10 J
Q K
A
Version A KEY – Page 2 of 17
Test 3
Version A KEY
MATH 1010
Essential Mathematics
Fall 2015
Sections 6A – 7C
Student’s Printed Name: _____________________ XID: C___________
Instructor: _________________________________ Section: _________
No questions will be answered during this exam.
If you consider a question to be ambiguous, state your assumptions in the margin
and do the best you can to provide the correct answer.
You have 90 minutes (1.5 hours) to complete this test.
General Directions:
•
Any communication with any person (other than the instructor or a designated
proctor) during this exam of any form, including written, signed, verbal, or digital,
is understood to be a violation of academic integrity.
•
All devices, such as computers, cell phones, cameras, and PDAs, must be
turned off while the student is in the testing room.
•
You may use any scientific calculator except a TI-89 or a TI-NSpire CAS.
•
No part of this test may be removed from the examination room.
On my honor, I have neither given nor received inappropriate or unauthorized
information at any time before or during this test.
Student’s Signature:________________________________________________
Do not write below this line.
Question
1
2
3
4
5
Scantron
Points
7
8
7
8
9
1
Earned
Free Response Total
40
Multiple Choice Total
60
Test Score
Version A KEY – Page 3 of 17
MATH 1010
Essential Mathematics
Test 3
Version A KEY
Fall 2015
Sections 6A – 7C
Multiple Choice Portion
There are 20 multiple choice questions. Each question is worth 3 points and has one
correct answer. Use a number 2 pencil and bubble in the letter of your response on the
Scantron sheet. For your own record, also circle your choice on your test since the
Scantron will not be returned to you. Only the responses recorded on your Scantron
sheet will be graded.
1.
Calculate the standard deviation for the following data: 1, 1, 3, 5, 8.
Round your answer to two decimal places.
A) Standard Deviation = 1.00
B) Standard Deviation = 8.80
C) Standard Deviation = 3.50
D) Standard Deviation = 2.97
E) Standard Deviation = 3.60
2.
How many different choices do you have in total if you buy a new Apple product
that is available in 6 colors and 2 styles?
A) 12
B) 6
C) 2
D) 8
E) 3
3.
The quiz scores for a class are given below. Find the mean, median, and mode of
the quiz scores.
4, 4, 5.5, 6, 7, 7.5, 8, 8.5, 9, 10
A) mean = 7, median = 7.5, mode = 4
B) mean = 6.95, median = 7, mode = 10
C) mean = 6.95, median = 7.25, mode = 4
D) mean = 6.25, median = 7.25, mode = 10
E) mean = 7.25, median = 7, mode = 7.5
Version A KEY – Page 4 of 17
Test 3
Version A KEY
MATH 1010
Essential Mathematics
4.
Fall 2015
Sections 6A – 7C
There are 5 white balls, 6 black balls and 7 yellow balls in a box. Suppose you
randomly select one ball from the box. Find the probability of choosing a ball that is
not black.
A) 1/2
B) 7/18
C) 2/3
D) 1/6
E) 1/3
5.
6.
Which of the distributions is skewed to the left?
A)
B)
D)
E)
C)
A roulette wheel has 38 numbers: 18 black numbers, 18 red numbers, and the
numbers 0 and 00 in green. Assume that all possible outcomes have equal
probability. If patrons in a casino spin the wheel 100,000 times, how many times
would you expect to see a red number? Round your answer to the nearest hundred.
A) 50,000
B) 2,600
C) 47,400
D) 46,200
E) 100,000
Version A KEY – Page 5 of 17
MATH 1010
Essential Mathematics
7.
Test 3
Version A KEY
Fall 2015
Sections 6A – 7C
Suppose you randomly draw 4 cards one at a time from a standard 52-card deck
and the deck is shuffled each time after the drawn card is returned. What is the
approximated probability that your first card is a Diamond, your second card is a
Spade, and your third and fourth cards are both Clubs?
(HINT: See formula sheet for standard deck of cards.)
Give your answer as a decimal rounded to four decimal places, if necessary.
A) 0.0039
B) 0.0154
C) 0.25
D) 0.0769
E) 0.0125
8.
An insurance policy sells for $1000. Based on past data, an average of 1 in 50
policyholders will file a $10,000 claim, an average of 1 in 100 policyholders will file
for $25,000, and an average of 1 in 250 policyholders will file for $60,000. So on
average, the company expects to profit how much per policy?
(HINT: You may find completing the following table helpful, but it is not required.)
Event
Value
$
$
$
$
Probability
Value × Probability
$
$
$
$
A) $1690
B) $1290
C) $1190
D) $310
E) $1210
Version A KEY – Page 6 of 17
MATH 1010
Essential Mathematics
9.
Test 3
Version A KEY
Fall 2015
Sections 6A – 7C
Which of the following statements is true about the normal distribution?
A) The distribution has multiple peaks.
B) The distribution is skewed to the left.
C) The mean is greater than the median.
D) Data values are spread evenly around the mean.
E) Large deviations from the mean are common.
10. Which measure of the center of a distribution is most affected by an outlier?
A) Median
B) Upper Quartile
C) Mode
D) Lower Quartile
E) Mean
11. Select the choice below to fill in the blanks in the following statement.
A false negative occurs when the test ______ returns a result of ______.
A) Correctly, positive
B) Correctly, negative
C) Correctly, inconclusive
D) Incorrectly, negative
E) Incorrectly, positive
Version A KEY – Page 7 of 17
Test 3
Version A KEY
MATH 1010
Essential Mathematics
Fall 2015
Sections 6A – 7C
12. The table below shows the result of a polygraph test conducted on 2000 college
students. Students were asked if they had ever cheated on a test. All of them
denied having cheated. Use the table below to answer the question.
Test finds student lying
Test finds student truthful
Total
Student has
actually cheated
83
14
97
Student has
actually not cheated
199
1704
1903
Total
282
1718
2000
Of those students who took the polygraph test and were found to be lying, what is
the percentage of students who had actually cheated?
A) 70.6%
B) 29.4%
C) 85.6%
D) 89.5%
E) 14.4%
13.
Given the box plot below, determine the upper quartile of the data set.
2
3
4
5
6
7
8
A) Q3 = 3
B) Q3 = 6
C) Q3 = 2
D) Q3 = 4
E) Q3 = 7
Version A KEY – Page 8 of 17
MATH 1010
Essential Mathematics
Test 3
Version A KEY
Fall 2015
Sections 6A – 7C
14. Suppose you randomly draw a card from a standard 52-card deck. What is the
probability that you pick a Heart or a Club?
(HINT: See formula sheet for a standard deck of cards.)
Round your answer to three decimal places, if necessary.
A) 0.5
B) 0.04
C) 0.25
D) 0.308
E) 0.326
15. Consider a study in which a diagnostic test is given to 100,000 people. We know
that 0.2% of the people will have a certain disease. This diagnostic test is 95%
accurate. How many people of the 100,000 have the disease and, among those,
how many were correctly identified by the test?
A) 2000 people have the disease; 1900 were correctly identified by the test.
B) 20000 people have the disease; 19000 were correctly identified by the test.
C) 200 people have the disease; 190 were correctly identified by the test.
D) 200 people have the disease; 200 were correctly identified by the test.
E) 200 people have the disease; 10 were correctly identified by the test.
16. John estimated his chance of winning his single-player tennis match is 70%. What
type of probability is this?
A) Subjective
B) Empirical
C) Objective
D) Conditional
E) Theoretical
Version A KEY – Page 9 of 17
MATH 1010
Essential Mathematics
Test 3
Version A KEY
Fall 2015
Sections 6A – 7C
17. The lifespans of lizards in a zoo are normally distributed. The average lizard lives
3.5 years and the standard deviation is 0.4 years. Approximately what percentage
of lizards live between 4.3 and 4.7 years?
A) 15.85%
B) 34%
C) 2.35%
All students were given credit for this problem because,
depending upon the technique used, the answer could be either
2.35% or 2.15% which is not given as a choice.
D) 0.15%
E) 2.5%
18. The grades for a chemistry midterm at Clemson are normally distributed with a
mean of 75 and a standard deviation of 4.25. Stephanie made an 82 on the exam.
What is the z-score for Stephanie’s exam grade?
Round your answer to the nearest hundredth.
A) z = 1.65
B) z = 1.04
C) z = –1.65
D) z = 0.86
E) z = –1.04
Version A KEY – Page 10 of 17
MATH 1010
Essential Mathematics
19.
Test 3
Version A KEY
Fall 2015
Sections 6A – 7C
Characterize the distribution shown below.
A) Unsymmetric, bimodal
B) Right-skewed, unimodal
C) Left-skewed, unimodal
D) Right-skewed, bimodal
E) Symmetric, unimodal
20. What is the probability of choosing the incorrect answers on the first three
consecutive questions on a multiple choice test if random guesses are made and
each question has 5 possible answers?
A)
1
25
B)
64
125
C)
16
125
D)
4
5
E)
1
5
Version A KEY – Page 11 of 17
Test 3
Version A KEY
MATH 1010
Essential Mathematics
Fall 2015
Sections 6A – 7C
Free Response Portion
Show all necessary work. Verify that the answers carry the appropriate units.
Partial credit may be given for work towards the correct solution.
However, if answers are shown without necessary work,
YOU MAY RECEIVE LITTLE OR NO CREDIT FOR THE CORRECT ANSWER.
1.
Suppose students in class had the following grades at the end of the year.
42, 56, 63, 66, 70, 72, 75, 75, 78, 78, 80, 92, 100
a.
Find the five-number summary for this set of data.
Round your answers to one decimal place.
42
Min: _____________
1 point per value in five-number summary
64.5
Lower Quartile (Q1): _____________
75
Median (Q2): _____________
79
Upper Quartile (Q3): _____________
100
Max: _____________
b.
Draw a box plot for the data set.
40
50
60
70
80
90
100
Student Grades
1 point for correct box plot format (Median may be double bar or bold or not.)
1 point for aligning plot to answers from part a, following work
Points earned on this question:
Available points on this question:
7
Version A KEY – Page 12 of 17
Test 3
Version A KEY
MATH 1010
Essential Mathematics
2.
Fall 2015
Sections 6A – 7C
Suppose you took a standardized test and the scores were normally distributed with
a mean of 75.25 points and a standard deviation of 7.38 points.
Directions: Round all z-scores to the nearest z-score in the table.
a.
Find your percentile given that your score was 89.5 points.
Round your final answer to the nearest hundredth.
z =
89.5 − 75.25
= 1.93 Use z = 1.9.
7.38
Table
97.13rd percentile
1 point for z-score
1 point for percentile (using table or calculator with some work shown)
b.
97.13rd
Answer: _________
percentile
If 5000 students took the test, how many would you expect to score above 88
points? Round your final answer to the nearest whole number.
88 − 75.25
Table
= 1.73 Use z = 1.7.
95.54th percentile
7.38
Percentage scoring above 88 points = (100 – 95.54)% = 4.46%
# of students ≈ .0446 × 5000 = 223
z=
1 point for z-score
1 point for percentage (using table or calculator with some work shown)
1 point for multiplying percentage by the total number of students
–½ if answer not rounded correctly
c.
223
Answer: _________
students
If your friend took the same test and scored in the 40th percentile, what was her
test score? Use the closest percentile in the table.
Round your final answer to the nearest whole number.
40th percentile
x − 75.25
–.25 =
7.38
Table
z ≈ –.25
x = (–.25)(7.38) + 75.25 = 73.41 ≈ 73
1 point for estimating z-score from percentile
(Award full credit for using calculator to get a better z-score estimate.)
1 point for setting up the z-score formula, following work
1 point for solving the equation for test score
–½ if answer not rounded correctly
73
Answer: _________
points
Points earned on this question:
Available points on this question:
8
Version A KEY – Page 13 of 17
MATH 1010
Essential Mathematics
3.
Test 3
Version A KEY
Fall 2015
Sections 6A – 7C
A bag contains 5 green marbles, 6 black marbles, 6 white marbles, and 3 green
common stones. You randomly draw one item from the bag.
State all answer as decimals rounded to one decimal place, if necessary.
a.
What is the probability of drawing a green item?
P(green) = 8/20 = .4
1 point for probability, work not required (Partial credit may be awarded for work.)
(½ point for numerator, ½ point for denominator)
–½ if answer not stated as a decimal
.4
P(green item) = _________
b.
What is the probability that you draw a black or a white marble?
P(black marble OR white marble)
P(black marble) + P(white marble) = 6/20 + 6/20 = 12/20 = .6
2 points for probability, work not required (Partial credit may be awarded for work.)
1 point for selecting events as non-overlapping
–½ if answer not stated as a decimal
.6
P(black marble OR white marble) = _________
The events are …
c.
Circle one: Overlapping
OR
Non-overlapping
What is the probability that you draw a green item or a marble?
P(green OR marble)
P(green) + P(marble) – P(green marble) = 8/20 + 17/20 – 5/20 = 20/20 = 1
2 points for probability, work not required
1 point for selecting events as overlapping
(Partial credit may be awarded for work.)
–½ if answer not stated as a decimal
1
P(green item OR marble) = _________
The events are …
Circle one: Overlapping
OR
Non-overlapping
Points earned on this question:
Available points on this question:
7
Version A KEY – Page 14 of 17
Test 3
Version A KEY
MATH 1010
Essential Mathematics
4.
Fall 2015
Sections 6A – 7C
An extensive study of 120 fun size packs of chocolate was done to determine the
average number of white chocolate per pack. The study found that a pack has at
most 5 white chocolate. The table below is a summary of the study.
Number of white
chocolate per pack
Frequency
0
3
1
18
2
3
53
24
4
5
15
7
Complete the table below to find the expected value of white chocolate per pack.
Leave probability column as unreduced fractions. Round other answers to three decimal places.
Value
(# white chocolate per pack)
Probability
1
18/120
3
24/120
0
2
4
5
3/120
53/120
15/120
7/120
Value × Probability
0
.15
.883
.6
.5
.292
2.425
Expected Value = ____________
white chocolate per pack
½ point per value in table, following reasonable work to the last column
2 points for expected value, following reasonable work from table
–½ if answer not rounded correctly
Points earned on this question:
Available points on this question:
8
Version A KEY – Page 15 of 17
MATH 1010
Essential Mathematics
5.
Test 3
Version A KEY
Fall 2015
Sections 6A – 7C
The table below shows the results of a study examining the effectiveness of home
schooling as compared to traditional schooling. The same reading test was given to
all students regardless of age group (10th grade or 12th grade).
10th Grade
12th Grade
a.
Home schooled
Passed
Failed
78
222
98
2
Traditional
Passed
Failed
25
75
287
13
Complete the table below by calculating the following percentages. For each
age group, determine the percentage passing the test for those schooled at
home and for those with traditional schooling. Combine the two age groups and
then determine the percentage passing the test for those schooled at home and
for those with traditional schooling.
Round your answers to the nearest tenth of a percent.
10th Grade
12th Grade
AGE GROUPS COMBINED
b.
Home schooled
78 / 300 = 26%
Traditional
25 / 100 = 25%
98 / 100 = 98%
287 / 300 = 95.7%
176 / 400 = 44%
312 / 400 = 78%
1 point per correct percentage in table (may award ½ credit for partially correct)
Complete the following explanation of why this is an example of Simpson’s
Paradox by filling in the blanks below with “HIGHER” or “LOWER”, as
appropriate.
1 point per correct completion of phrase
HIGHER
A ____________
percentage of home schooled students passed considering
the individual age groups (10th grade and 12th grade),
LOWER
but, a _____________
percentage of home schooled students passed when
considering the age groups combined.
c.
What design flaw in the study caused Simpson’s Paradox to occur?
Circle the Roman Numeral of your choice.
I.
The traditional students must have been chosen from the better schools
available for the study.
II.
There aren’t enough students in the study.
1 point for correct choice
III. The group of home schoolers is comprised of mostly 10th graders, while the
group of traditional students is mostly 12th graders.
Points earned on this question:
Available points on this question:
9
Version A KEY – Page 16 of 17
MATH 1010
Essential Mathematics
Test 3
Version A KEY
Fall 2015
Sections 6A – 7C
Scantron (1 pt.)
Check to make sure your Scantron form meets the following criteria. If any of the
items are NOT satisfied when your Scantron is handed in and/or when your
Scantron is processed one point will be subtracted from your test total.
My Scantron:
□ is bubbled with firm marks so that the form can be machine read;
□ is not damaged and has no stray marks (the form can be machine read);
□ has 20 bubbled in answers;
□ has MATH 1010 and my Section number written at the top;
□ has my Instructor’s name written at the top;
□ has Test No. 3 written at the top;
□ has Test Version A both written at the top and bubbled in below my CUID;
□ and shows my correct XID written in and then bubbled in with a zero in the first
column followed by the eight digits.
Version A KEY – Page 17 of 17