MATH 107
Practice Test 4
Chapters 5(Sec. C), 6(Sec. A – C)
1.The following data are exam scores achieved by the students in a physics class. Arrange the data into
a stem-and-leaf display(plot).
79 43 65 84 77 70 52 61 80 66 68 48 55 78 71 38 45 64 67 73
77 50 67 91 84 33 49 61 72
2. Heights of women have a mean of 63.6 inches and a standard deviation of 2.5 inches. Erin Zito has
a height described by z= -1.25. What is her height in inches?
3. Find the following:
a) P(Z<1.58)
b) P(-2.3<Z<-1.45)
4. The speed, in miles per hour, of twenty randomly monitored cars on an interstate near Las Vegas,
Nevada, were as follows:
66
80
71
63
64
84
61
64
73
66
78
70
74
65
67
76
70
58
65
72
a) Create a grouped relative frequency distribution with 5 classes.
b) Using your frequency distribution above, construct a histogram of the data.
5. Classify the following types of data as discrete or continuous.
a) number of cars
b) weight of a couch
6. The volume of liquid in a bottle of eye drop medicine is normally distributed with a mean of 30.5 ml
and standard deviation of 2.5 ml. Calculate the following probabilities of randomly selecting a bottle:
a) with less than 32 ml of eye drop medicine.
b) with more than 28.5 ml of eye drop medicine.
c) with the amount of eye drop medicine between 26.5 and 34 ml.
7. The following frequency distribution lists the number of hours per day that a randomly selected
sample of teenagers spent watching television.
X=hours per day
0.0  x<2.0
2.0  x<4.0
4.0  x<6.0
6.0  x<8.0
8.0  x<10.0
Number of teenagers
45
33
58
30
7
Where possible, determine what percent of the teenagers spent the following number of hours
watching television.
a) At least 4 hours.
b) Between 3 and 4 hours.
c) At least 2 hours, but less than 6 hours.
8. The following data represent the hourly wages of the ten employees at the Fresh Wine Co.:
$4.50 $4.75 $15.50 $4.75 $7.50 $4.50 $6.50 $6.25 $50.00 $4.75
a)
b)
c)
d)
Find the mean wage.
Find the median wage.
Find the mode wage.
Does the mean honestly represent the "average"? Why or why not?
9. The shrinkage in length of a certain brand of blue jeans is normally distributed with a mean of 1.35
inches and standard deviation of 0.25 inch. What percent of this brand of jeans will shrink between 1
and 2 inches?
10. Find the grade point average(GPA) for the following student. Assume A = 4, B = 3, C = 2, D = 1,
and F = 0. Round your answer to the nearest hundredth.
COURSE
Math 115
Art 105
PE 201
Engl 101
CREDITS
5
3
2
4
GRADE RECEIVED
B
A
A
C
11. Use the stem-and-leaf display to answer the following questions:
Stem
2
2
3
3
4
4
5
5
6
Leaves
3
6
0
5
1
5
2
8
0
a)
b)
c)
d)
e)
3
7
1
6
2
7
4
4
8
1
7
2
9
9
2
8
4
9
3
8
3
9
3
4
Compute the median.
Compute the mode(s), if any.
Compute the range.
Compute the third decile, 𝐷3 .
Compute the eighty-fifth percentile.
12. The grade point average of the senior class of Jefferson High School is normally distributed with a
mean of 2.7 and a standard deviation of 0.4 point. If a senior in the top 10% of his or her class is
eligible for admission to any of the nine campuses of the State University system, what is the
minimum grade point average that a senior should have to ensure eligibility for admission to the
State University system?
13. An analysis of train derailment incidents showed that 23 derailments were caused by bad track, 9
were due to faulty equipment, 12 were attributable to human error and 6 had other causes (based on
data from the Federal Railroad Administration). Construct a pie chart representing the given data.
14. During the 2005 Major League Baseball season, each team played a total of 162 regular season
games. The tables below show the statistics on games won for all three divisions of both leagues.
In each case, n = number of teams in the division, 𝑥̅ = average (mean) number of games won, and
s = standard deviation of number of games won.
American League
East Division
n=5
𝑥̅ = 82.2
s = 12.6
Central Division
n=5
𝑥̅ = 80.4
s = 17.3
West Division
n=4
𝑥̅ = 82.8
s = 11.3
National League
East Division
n=5
𝑥̅ = 85.0
s = 3.8
Central Division
n=6
𝑥̅ = 81.5
s = 11.7
West Division
n=5
𝑥̅ = 74.4
s = 5.7
a)
Overall, who had the greatest winning average, the East teams, the Central teams, or the
West teams?
b) Overall, where were the teams the least “consistent” in number of games won, East, Central
or West?
c) The Cleveland Indians, in the Central Division of the American League, won 93 games,
while the Philadelphia Phillies, in the East Division of the National League, won 88 games.
Use z-scores to determine which of these two teams did relatively better within its own
division of 5 teams.
Know your terminology:
Bell curve
decile
Frequency
frequency table
Midrange
quartile
Mode
normal distribution
Sample
relative frequency
standard deviation
standard normal distribution
descriptive statistics
histogram
percentile
outlier
statistics
Empirical Rule
categorical data
deviation
pie chart
mean
population
variance
discrete data
discrete variable
inferential statistics
median
numerical data
z-score
continuous data
Math 115
Practice Test #4 Answers
Chapter 13
1.
Stem
3
4
5
6
7
8
9
Leaves
3
3
0
1
0
0
1
8
5
2
1
1
4
2. 60.5 inches
3.a. 0.9429 b. 0.0628
4.a.
Speed(mph) X
58  X  64
64  X  70
70  X  76
76  X  82
82  X  88
8
5
4
2
4
9
5
3
Frequency
3
7
6
3
1
6
7
7
7
Relative Frequency
0.15
0.35
0.30
0.15
0.05
b.
10
Freq.
5
58 64 70 76 82 88
Speed(mph)
5.a. discrete b. continuous
6.a. 0.7257 b. 0.7881 c. 0.8644
7.a. approx. 54.9% b. Cannot be determined c. approx. 52.6%
8.a. $10.90 b. $5.50 c. $4.75
9. 91.5%
10. 3.07
7
8
8
9
11.a. 35
12. 3.2
13.
b. 33
c. 37
d. 31
Faulty Bad
Other causes 18% Track
12%
Human Error-24%
46%
14.a. East
b. Central
c. Phillies
e. 49