Math 160
Chapters 1 – 4
NAME: __ ______
DIRECTIONS: Create a word document titled Midterm (your last name). Most of
the work and answers can be created with Word. All work is expected to be your
own. Any questionable papers will not be graded and a failing grade will be given.
EXPRESS PROBABILITY AS A REDUCED FRACTION OR TO 4 DECIMAL
PLACES. SHOW ALL APPROPRIATE WORK. IF ALL YOU HAVE IS THE
ANSWER, I CAN NOT AWARD ANY PARTIAL CREDIT.
I. Short Answer (#1 – 21)
1.)Statistics is the science of conducting studies to
A) solve a system of equations.
B) hypothesize, experiment, and form conclusions.
C) collect, organize, summarize, analyze, and draw conclusions from data.
D) monitor, study, and report on a subject.
2.) Which of the following correctly describes the relationship between a sample and a
population?
A) A sample is a group of populations that are subject to observation.
B) A population is a group of samples that may or may not be included in a study.
C) A sample is a group of subjects selected from a population to be studied.
D) A population and a sample are not related.
3.) If a researcher manipulates one of the variables and tries to determine how the
manipulation influences other variables, the researcher is conducting what kind of
study? Experimental Study
4.) What level of measurement classifies data into mutually exclusive (nonoverlapping),
exhausting categories in which no order or ranking can be imposed on the data? Nominal
5.) Give an example of systematic sampling. Do not use any examples given in
textbook. If Food Lion wanted to study the buying habits of their customers. They could
then choose every 10th to study.
6.) True or False: Inferential statistics is based on probability theory. T
7.) Classify each of the following as quantitative or qualitative. If it is quantitative, tell
whether it is discrete or continuous.
a.) Number of donuts sold at Dunkin Donuts on Monday. Quantitative, Discrete
b.) Weights of fish caught in New River. Quantitative, continuous
c.) Colors of baseball caps in a store. Qualitative
d.) Marital status of faculty members in a large university. Qualitative
e.) Lifetime of 12 flashlight batteries. Quantitative, continuous
8.) In an ad for a car, a driver is shown driving expertly through a difficult road course.
At the bottom of the ad, the following is included in small print "Professional driver on
a closed course). This is an example of
A) changing the subject
C) suspect samples
B) detached statistics
D) implied connections
9.) A weatherman records the amount of rain that has fallen in Portland, Oregon during
each day. What type of graph should he use?
A) pie graph B) pictograph C) time series graph D) ogive
10.) True / False: An ogive graph is also called a cumulative frequency graph.
11.) A pie graph was created showing the number of children per family. If 175 families
were in the survey and the section depicting families with three children represented
105°, the number of families with three children was ___. Show how you got this
answer.
12.) If data is clustered at one end or the other, it indicates that there is a skewed
distribution.
13.) Which of the following is a histogram? Answer is D
A)
B)
C)
D)
14.) A normal distribution in which approximately 68% of the data values fall within
one standard deviation of the mean behaves according to the Empirical rule.
A) the empirical rule.
C) a boxplot.
B) a symmetrical distribution.
D) differential statistics.
15.) Find the z score for each student and indicate which one is higher. Show your
work!!
Z= value- mean/standard deviation
a.) A score of 3.2 on a test with a mean of 4.6 and a standard deviation of 1.5. 3.24.6=-1.4/1.5= -.62 is z and this is also the higher one out of them
b.) A score of 630 on a test with a mean of 800 and a standard deviation of 200.
630-800= -170/200= -0.85 is z
c.) A score of 43 on a test with a mean of 50 and a standard deviation of 5.
43-50= - 7/ 5= - 1.4 is z
16.) Which of the following is true?
A) D5  P5  Q5 B) D50  P5  Q25 C) D5  P50  Q2
D) D50  P5  Q2
17.) True / False: A five-number summary of a data set consists of the minimum, Q1 , the
mean, Q3 , and the maximum.
18.) Find the weighted mean for three exams if the first one was worth 95 points and the
student received a score of 78%, the second was worth 50 points and the student received
a score of 88% and the third was worth 45 points and the student received a score of
95%? Show your work. Answer= 78.1
0.7 * 75 = 52.5
0.8 * 50 = 40
0.95 * 30 = 28.5
(52.5 + 40 + 28.5)/(75 + 50 + 30) = 0.7806
19.) If a sample of data has mean 40 and variance 81, then it's coefficient of variation is?
Show your work.
20.) The staff at a small company includes: 4 secretaries, 20 technicians, 4 engineers, 2
executives, and 50 factory workers. If a person is selected at random, what is the
probability that he or she is a factory worker? Show your work. The total number of
them is 80. 50 factory workers. Which would be 50/80 reduced is 5/8
1
A) 4
1
B) 8
5
C) 8
2
D) 5
21.) In a recent study, the following data was obtained in response to the question, “Do
you favor recycling in your neighborhood?”
Yes
No
No Opinion
Males
25
15
10
Females
30
10
10
If a person is picked at random, what is the probability that the person is either male or
has no opinion regarding recycling? 25+15+10+ one group of no opinion from female is
10= 60 and its 100 of them in all so answer is 60/100 reduced is 3/5
Use for #22-24: A recent poll by the American Automobile Club found that 43% of
those surveyed are worried about aggressive drivers on the road. If three people are
selected at random, what is the probability that
22.) all three will be worried about aggressive drivers on the road? (0.3)^3=0.027
23.) at least one will be worried about aggressive drivers on the road?
24.) none will be worried about aggressive drivers on the road?
25.) How many different ways can four people: Andy, Betty, Cindy, and Doug, sit in a
row at the opera if Andy and Cindy must sit together? Answer = 12
Andy = A, Betty = B, Cindy = C, Doug=D
ABCD BACD
ABDC BADC
CABD CBAD
CDAB CDBA
DABC DBAC
DCAB DCBA
The following represents the ages of 30 customers who ordered a product advertised on
TV.
42
44
62
35
20
30
56
20
23
41
55
22
31
27
66
21
18
24
36
39
40
18
Using these data points:
36
22
42
25
32
50
31
26
26.) Construct a stem and leaf plot.
STEMS
1
2
3
4
5
6
LEAVES
8,8
0,0,1,2,2,3,4,5,6,7
0,1,1,2,5,6,6,9
0,1,2,2,4
0,5,6
2,6
27.) Using seven classes, complete the following frequency table using the data
above:
CLASS
FREQ
RELATIVE
CUM. REL.
CLASS
LIMITS
FREQ
FREQ
MARKS
18-24
9
9/30
9/30
21
25-31
6
6/30
15/30
28
32-37
39-45
46-52
53-59
60-66
4
6
1
2
2
4/30
6/30
1/30
2/30
2/30
19/30
25/30
26/30
28/30
30/30
34.5
42
49
56
63
28.) Using the data points given above, find the following measures to 2 decimal
places (If the answer is 55 you may either give 55 or 55.00)
a.) sample mean 9.78( ROUNDED)
( add all numbers together from top
Divide by 30 since 30 numbers)
b.) median
_31.50________
h.) Q1
_________
i.) Q3
_________
c.) mode 18,20,22,31,36,42
j.) IQR
d.) midrange
_________
k.) percentile rank of 42_________
e.) range
_________
l.) CVar
__________
_________
f.) sample
_________
standard deviation
g.) sample variance
_________
29.) Two distinct fair dice are rolled at the same time and the number of dots appearing
on both are counted. Find the probability that this sum is
A.) 7 there are 6 different ways to get 7 so 6/36 reduced is 1/6
B.) 5 or 9 getting a 5 is 4/36 getting a nine is 4/36 add the two = 8/36 reduced is 2/9
C.) at least 6 the ways getting this is 5, 6,5,4,3,2,1= 26 so 26/36 = 2/3 reduced
30.) A card is selected from an ordinary deck of 52 cards. What is the probability of
getting
A.) a club or a jack = 16/52=4/13
B.) a queen and an ace (no this is not a typo) = 0/52=0
C.) a diamond and a four= 1/52
Southwest Elementary School uses school buses supplied by companies A, B and C.
The probability that the busses supplied by company A arrive on time is 0.975, the
probability that the buses supplied by company B arrive on time is 0.95 and the
probability that the buses supplied by company C is late is 0.07. Find the probability
that
31..) all the busses arrive on time (hint: this means bus A and bus B and bus C all
arrive on time) = 0.975*0.95* (1-0.07)0.93=0.8614125=.86
32.) one of the buses arrives on time 4.62
33.) none of the buses arrive on time---- 1-0.975=0.025 b 1-0.95=0.05 c= 0.07 so I
multiply 0.025*0.05*0.07=0.0000875 is the answer
34.) at least one of the buses arrive on time (this is the compliment to #33) …. 10.0000875=0.9999125
35.) two of the buses arrive on time
36.) no more than one of the buses is late
MAKE SURE YOU LOOK AT MY NOTES POSTED UNDER COURSE
DOCUMENTS!!