Name
AP Statistics First Semester Exam Review
Chapter 1 Review
You want to know how often residents of cold climates vacation in warm destinations. You randomly sample 50
re,dents and find out how many annual trips to warm destinations they've taken during their adult lives.
an example
rÿ__ÿr False: This
is of discrete data.
.
Which of these are categorical data?
A. The birth weights of anteaters
B. The lengths of anteaters
The different types of anteaters
D. The top speeds of anteaters
E.
1
The prices of anteaters
Your class is participating in an Internet game show and must choose whether a prize is behind door #1 or
door #2. You take a vote. The numbers for the doors are an example of which kind of data?
A. Quantitative, discrete
jÿ,ÿ {ÿ
B. Quantitative, continuous
Cÿ Categorical
D. None of the above
.
When your class participates in an Internet game show and counts the votes for door #1 and door #2, the
counts are examples of what kind of data?
.-Quantitative,
Quantitative, continuous
discrete
C. Categorical
D. None of the above
5. Which of the following would most likely be graphed as a bar chart rather than a histogram?
A. The number of blue, red, black, and white cars in a random sample of 500 cars
B. The number of students in a mid-size university who own Macintosh or PC computers
C. The ethnic distribution for a major city
D. The number of people in various management positions at a large electronics store
All of the above
6. The paper "Lessons from Pacemaker Implantations" gave the results of a study that followed 89 heart
patients who had received electronic pacemakers. The time (in months) to the first electrical malfunction of
the pacemaker was recorded.
24 20 16 32 14
24 14 20 18 14
12 24 6 12 18
12 12 8 24 10
26 20 6 14 16
22 28 24 30 34
22
16
16
14,
18
26
2 12
18 20
34 18
16 22
24 18
24 22
24
22
20
24
16
28
6
24
22
22
6
30
10
26
24
20
16
22
20
28
26
24
10
24
a. Create a frequency table and relative frequency histogram.
b. Create an ogive
8
18
18
28
14
22
16 12
14 10
2 18
20 22
18 24
32
You're the manager of the packing crew at Meatin° Place meat market, where the slogan is "no customer is an
outlier." Being the manager, you spend your time weighing meat packages and creating five-number summaries.
Here are some ground beef package weights, in pounds:
0.75
0.83
0.99
1.06 1.08 1.08 1.15 1.16 1.16 1.19 1.19 1.2
1.28
1.38 1141
.
0.87
0.89
0.89
0189
0.92
0.93
0.96
0.96
0.97 0.98
1.21 1.24
io]ÿII ÿ/ÿ.ÿ|ÿ l,ÿi l/lÿ
Create a stemplot of the data. Don't round to whole numbers. They will all be l's!
,q
I,u
1,1
1,)
1.'i
o l ,t
I
8. Calculate the mean, median and mode. Do the mean and median values support the shape of the distribution?
9. Calculate the five number summary and draw a boxplot.
•
7
5"
,
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l,U
,
i
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,
"
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10. In the package weight data you know that an outlier would have a"ÿ
weight-:"
[ÿ" ÿ ÿ/ÿ" Iÿ I,X /(Vÿ
A. below 1 pound.
B. between the minimum weight and the weight at the lower quartile (Q1).
C. above 1.2 pounds.
D. below the lower quartile weight.
None of the above
Chapter 2 Review
.
Suppose the distribution of GPAs at Jefferson High School has a mean of 2.7 and a standard
deviation of 0.37. The GPAs at Washington High School has a mean of 2.8 and a standard
deviation of 0.33.
Ted, a student at Washington High School, has a GPA of 3.25, and Frank, at Jefferson
High School, has a GPA of 3.17. Calculate the z-score for Ted and Frank and comment on
which of them has the higher GPA relative to his peers.
b.
What GPA would Ted need to have the same z-score as Frank? "-3', ÿ'-ÿ
c. Torsten, another student at Jefferson High School, has a GPA of 3.07. Assuming that
these GPAs follow a mound-shaped distribution, approximately what proportion of
Jefferson High School students,have a1larger GPA? (Use the empirical rule to answer
this question.) ÿ --(
/ÿ¢ ÿ ÿ Iÿ, ÿ'd°.ÿ
d. What GPÿwould you need to have to be in the top 10% of the class at each high school?
.
Suppose the average height of women collegiate volleyball players is 5'9", with a standard
deviation of 2.1". Assume that heights among these players follow a mound-shaped distribution.
a. According to the empirical rule, about 95% of women collegiate volleyball players have
heights between what two values?
(ÿ,ÿ - -).ÿ ,,,k
b. What does the empirical rule say about the proportion of players who are between 62.7
inches and 75.3 inches? ÿ, ÿ<ÿ ÿuÿ(/t ÿ /-ÿt/L/ÿ,ÿ
c. Reasoning from the empirical rule, what is the tallest we would expect a woman collegiate
volleyball player to be? 6tÿ)cÿ'ÿ ÿ7ÿ',ÿ ; ÿ ÿ1ÿ;ÿ CÿJfÿ/'ÿ'/'ÿ 4ÿt'ÿ,t
.
Data from the National Vital Statistics Report reveal that the distribution of the duration of
human pregnancies (i.e., the number of days between conception and birth) is approximately
normal with mean ÿ = 270 and standard deviation a = 15. Use this normal model to determine
the probability that a given pregnancy comes to term in:
a. less than 244 days (which is about 8 months). ,ÿ Lÿ
b. more than 275 days (which is about 9 months). ; :37ÿ'7
c. over 300 days.
, (Pÿ,-I
d. between 260 and 280 days. .. ÿ(ÿ ÿ(
e. Data from the National Vital Statistics Report reveal that of 3,880,894 births in the US
in 1997, the number of pregnancies that resulted in a preterm delivery, defined as 36 or
fewer weeks since conception, was 436,600. Compare this to the prediction that would
be obtained from the model. ÿ -ÿ /l,/, ÿ
.
ÿ ÿ "ÿ
L
Suppose that you are deciding whether to take Professor Fi'sher's class or Professor Savage's
next semester. You happen to know that each professor gives A's to those scoring above 90 on
the final exam and F's to those scoring below 60. You also happen to know that the distribution
of scores on Professor Fisher's final is approximately normal with mean 74 and standard/.ÿlC"
deviation 7 and that the distribution of scores of Professor Savages final is approximaÿ ,ÿ,
normal with mean 78 and standard deviation 18.
ÿ'ÿ
a. Produce a sketch of both teachers grade distributions, on the same scale. ÿ-- ÿ
1
b. Which professor gives the higher proportion of A's? Show the appropriate calculations
to support your answer.
<ÿ"ÿoÿ'ÿ ,1ÿ,ÿ ÿ ,cC(
c. Which professor gives the higher proportion of F's? Show the appropriate calculations
to support your answer. ÿ'ÿ ,/ÿ '7 ? rÿ" Jÿ>-
d. Suppose that Professor DeGroot has a policy of giving A's to the top 10% of the scores
on his final, regardless of the actual scores. If the distribution of scores on his final
turns out to be normal with mean 69 and standard deviation 9, how high does your score
have to be to earn an A?
,
ÿ/ÿ FSÿj ÿ-ÿ
Suppose that the IQ scores of students at a certain college follow a normal distribution with
mean 115 and standard deviation 12.
,/ÿ Iÿ
a. Draw a sketch of this distribution. Be sure to label the horizontal axis..
b. Shade in the area corresponding to the proportion of students with an IQ-'b'elow 100".'
Based on this shaded region, make an educated guess as to this proportion. ÿ,/S" "/ÿ
c. Use the normal model to determine the proportion of students with an IQ score below
Ioo.
d. Find the proportion of these undergraduates having IQs greater than 130. ÿ ÿ(ÿ' ÿ'ÿ;
e. Find the proporti0n of these undergraduates having IQs between 110 and 130. ÿ 4ÿ'ÿ- ÿ"
f. With his IQ of 75, what would the percentile of Forrest Gump's IQ be? /ÿtÿvr_ÿL/ÿ'
g. Determine how high one's IQ must be in order to be in the top 1% of all IQs at this
college.
ÿL 7__(I'ÿ
"
.
Suppose that Professors Wells and Zeddes have final exam scores that are approximately
normally distributed with mean 75. The standard deviation of Wells' scores is 10, and that of
Zeddes' scores is 5.
a. With which professor is a score of 90 more impressive? Support your answer with
appropriate probability calculations and with a sketch. ÿ.ÿL>I, ÿ_ = 3 > ÿ =/- l
b. With which professor is a score of 60 more discouraging? Again support your answer
with appropriate probability calculations and with a sketch.ÿ-ÿcÿÿ ÿ - -ÿ ÿ ÿ ÿ ÿ/, J-
.
Suppose that the wrapper of a certain candy bar lists its weight as 2.13 ounces. Naturally, the
weights of individual bars vary somewhat. Suppose that the weights of these candy bars vary
according to a normal distribution with mean ÿ = 2.2 ounces and standard deviation ÿ = 0.04
ounces.
a. What proportion of candy bars weigh less than the advertised weight? td,ÿcfoJ
b. What proportion of candy bars weigh more than 2.25 ounces? ,(d ÿ.ÿ
c. What proportion of candy bars weigh between 2.2 and 2.3 ounces? , ÿ ci'.ÿ"
d. If the manufacturer wants to adjust the production'process so that only 1 candy bar in
1000 weighs less than the advertised weight, what should the mean of the actual weights
be (assuming that the standard deviation of the weights remains 0.04 ounces)?/(ÿ ÿo.,ÿ'ÿ
.
Sample data from the National Center for Health Statistics reveal that weights of American
men aged 20 - 29 have a mean of about 175 pounds and a standard deviation of about 35 poundSl
For women the mean is about 140 pounds and the standard deviation is about 30 pounds.
a. If these distributions are roughly normal, what percentage of men would you expect to
weigh less than 150 pounds? Less than 200 pounds? Less than 250 pounds?
, qv°)((
b. Answera. forwomen. , ÿJ(,Yÿ
ÿq'77ÿ-
,(-ÿ,ÿ
c. Sample data from the National Center for Health Statistics reveal that the observed
percentages in these ranges are 29.0%, 82.1%, and 96.2% for men, compared to 70.4%,
92.5%, and 99.0% for wom(m. How well does the normal model predict these
percentages? ÿ('ÿ IAÿ (ÿ/(ÿ/[
9. A person with too much time on his hands collected 1000 pennies that came into his possession
in 1999 and calculated the age (as of 1999) of each. The distribution has mean 12.264 years and
standard deviation 9.613 years. Knowing these summary statistics but without seeing the
distribution, can you comment on whether the normal distribution is likely to providÿ a
reasonable.
• ,m°del for these
penny_ .aqesÿ Explain/ . iiÿ ÿJÿ ÿ'1 { ÿ ÿltÿ {(" /
" "ÿ1 ,ÿÿ" ÿ" ÿlÿlÿ'ÿ ÿ'ÿ{ÿ/C( ÿ'/vÿ ÿ¢
10. Use the table of standard normal probabilities to determine the proportion of the normal curve
that falls within:
a. one standard deviation of its mean (in other words, between z-scores of -1 and 1). ,ÿ4ÿ-ÿ
b. two standard deviations from the mean (//cJÿ)c. three standard deviations from the mean. ( ÿic('/ÿ>
d. Compare these values to the values obtained from the empirical rule.
Chapter 3 Review
.
Foresters use regression to predict the volume of timber in a tree using easily measured quantities
such as diameter. Let y be the volume of timber in cubic feet and x be the diameter in feet
(measured at 3 feet above ground level). One set of data gives
y = -30 +60x.
The predicted volume for a tree of 18 inches is:
(a) 1050 cubic feet
(b) 600 cubic feet
(c) 105 cubic feet
(d) 90 cubic feet
(ÿ60 cubic feet
(f)
2.
Consider the following scatterplot of midterm and final exam gcores for a class of 15 students.
Which of the following are true statements?
Iÿam,,ÿorÿl
110100-
I.
The same number of students scored 100 on the midterm
exam as scored 100 on the final exam.
II.
Students who scored higher on the midterm exam tended
to score higher on the final exam.
ÿ
o
e
o o
7o
e
o
e
-- 50-
ÿ
o
o
o
o
30-
o
III. The scatterplot shows a moderate negative correlation
between midterm and final exam scores.
20
go do do
16o
IvtSterm_ÿam Scere
(a) I and II
I and III
(c) II and III
(d) I, iI, and III
(e) None of the above gives the complete set of complete true responses.
,
Data are obtained for a group of college freshman examining their SAT scores (math plus verbal)
from their senior year of high school and their GPAs during their first year of college. The
resulting regression equation is:
y=O.OO161x+l.35 with s =120 ,and s =.3057
What percentage of the variation in GPAs can be explained by looking at SAT scores?
(a) 0.161%
(b) 16.1%
(ÿ)) 39.97o
(d) 63.27°
(e) This value cannot be computed from the information given.
4.
Suppose the correlation between two variables is r = 0.23. What will the new correlation be if 0.14
is added to all values of the x-variable, every value of the y-variable is doubled, and the two
variables are interchanged?
(ÿ 0.23
(b) 0.37
(c) 0.74
(d) -0.23
(e) -0.74
5 1 Given the least-squares regression line:[Cost of a Monopoly Property] = 67.3 + 6.78 * [Spaces From
GO],
determine the residual for Reading Railroad which costs $200 and is 5 spaces from GO.
(a) -98.8
(b) -9.88
,.ÿ 98.8
(d) -1418.3
(e) A residual has no meaning since one of the variables is categorical.
6. A study of the fuel economy for various automobiles plotted the fuel consumption
(in liters of gasoline used per 100 kilometers traveled) vs. speed (in kilometers per hour).
A least-squares regression line was fitted to the data and the residual plot is displayed to
The right. What does the pattern of the residuals tell you about the linear model?
(a) The evidence is inconclusive.
(b) The residual plot confirms the linearity of the data.
(c) The residual plot suggests a different line would be more appropriate.
The residual plot clearly contradicts the linearity of the data.
(e) None of the above.
U
•
i n
0
0
.....
0
0
0001ÿ
71 The coefficient of determination of the data described in the scatterplot is:
(a) 0.35
(b) 0.65
L
e
n
g
t
h
(c) -0.80
0.88
2.4
2.0
1.6
1.2
N
o
0.8
.-
I
5
I
10
I
15
e
/
Number of Lies
I
20
8. With regard to regression, which of the following statements about outliers are true?
I.
Outliers have large residuals.
II.
A point may not affect the regression equation even though its x-value is
displaced in the x-direction and its y-value is an outlier in the y direction.
III.
Removal of an outlier will affect the regression line in a meaningful way.
(a) I and II
(b) I and III
)II and III
I, II, and III
(e) None of the above gives the complete set of true responses.
9,
As reported in the Journal of the American Medical Association (June 13, 1990), for a study of ten
nonagenarians, the following tabulation shows a measure of strength versus a measure of functional
mobility
Strength
7.5 6 11.5 10. 9.5 18 4
(kg)
9
3
5
Walk time 18 4 8
(s)
12
25 25 7
22 12
10
48
6
What does the slope of the least-squares regression line signify?
(a) The sign is positive, signifying a direct cause-and-effect relationship between strength and
mobility.
(b) The sign is positive, signifying that the greater the strength, the greater the functional mobility.
(c) The sign is negative, signifying that the relationship between strength and functional mobility is
weak.
dÿThe sign is negative, signifying that the greater the strength, the less the functional mobility.
(e) The slope is close to zero, signifying that the relationship between strength and functional mobility
is weak.
10. Consider the three points (2,11), (3,17), (and (4,29). Given any straight line, we can calculate the
sum of the squares of the three vertical distances from these points to the line. What is the
smallest possible value this sum can be?
(ÿ6
(b) 9
(c) 29
(d) 57
(e) cannot be determined
Part II - Free Response- Show your work and explain your results clearly.
11. (a) Find the equation of the least-squares regression line of
the data represented in the scatterplot at the right.
4-
>2-
1:
0
6
x
(b) Draw in the LSRL on the scatterplot using two points on either
extreme of the scatterplot. Record these points below.
(c) Calculate r and r2. What does r2 describe?
F, O
12. An analysis of the relationship between the number of telephones in a household (x) and the annual
family income(y) revealed the following statistics:
- = 3.8
m= 65,000
y
n = 26
sx=1.2
s.,=15,500
r=0.65
(a) Determine the least-squares regression line.
(b) Determine coefficient of determination. Explain what this index means.
•
Chapter 5 Review
1. Which of the following are true statements?
I.
If bias is present in a sampling procedure, it can be overcome by dramatically increasing the sample
size.
II.
There is no such thing as a "bad sample."
III. Sampling techniques that use probability techniques effectively eliminate bias.
A. I only
B. II only
.III only
D. None of the statements are true.
E. None of the above gives the complete set of true responses.
21 Which of the following are true statements?
I.
Voluntary response samples often over-represent people with strong opinions.
II.
Convenience samples often lead to undercoverage bias.
III.
Questionnaires with non-neutral wording are likely to have response bias.
(ÿI and II
B. I and III
C. II and III
D. I, II, and III
E. None of the above gives the complete set of true responses.
3. Consider the following events:
I.
Although 18% of the student body is minority, in a random sample of 20 students, 5 are minorities.
II.
In a survey about sexual habits, an embarrassed student deliberately gives the wrong answers.
III.
A surveyor mistakenly records answers to one question in the wrong space.
Which of the following correctly characterizes the above?
A.
I, random sampling error; II, response bias; III, human error
B.
I, random sampling error;ÿI, nonresponse bias; III, hidden error
C.
I, hidden bias; ÿ voluntary sample bias; III, sampling error
D.
I, undercoverage error,; II, voluntary error; III, unintentional error
I, small sample error; II, deliberate error; III, mistaken error
.
Each of the 29 NBA teams has 12 players. A sample of 58 players is to be chosen as follows. Each team will
be asked to place 12 cards with their players' names into a hat and randomly draw out two names. The two
names from each team will be combined to make up the samplel Will this method result in a simple random
O
sample of the 348 basketball players?
A. Yes, because each player has the same chance of being selected.
B. Yes, because each team is equally represented.
C. Yes, because this is an example of stratified sampling, which is a special case of simple random sampling.
No,because
becausethe
notteams
each group
ofchosen
58 players
has the same chance of being selected.
lÿ.ÿ No,
are not
randomly.
5. In designing an experiment, blocking is used
A. To reduce bias.
To reduce variation
C. As a substitute for a control group
D. As a first step in randomization
E. To control the level of the experiment.
.
A nutritionist believes that having each player take a vitamin pill before a game enhances the performance of
the football team. During the course of one season, each player takes a vitamin pill before each game, and
the team achieves a winning season for the first time in several years. Is this an experiment or an
observational study?
O
Aÿ. An experiment, but with no reasonable conclusion possible about cause and effect
B. An experiment, thus making cause and effect a reasonable conclusion.
C. An observational study, because there was no use of a control group.
D. An observational study, but a poorly designed one because randomization was not used.
E. An observational study, thus allowing a reasonable conclusion of association but not of cause and effectl
7. Which of the following are true about the design of matched-pair experiments?
I.
Each subject might receive both treatments.
II.
Each pair of subjects receives the identical treatment, and differences in their responses are noted.
Blocking is one form of matched-pair design.
III.
,ÿI only
B°
B. II only
C. III only
D. I and III
E. II and III
A consumer product agency tests miles per gallon for a sample of automobiles using each of four different
octane varieties of gasoline. Which of the following is true?
A. There are four explanatory variables and one response variable.
B. There is one explanatory variable with four levels of response.
C. Miles per gallon is the only'explanatory variable, but there are four response variables corresponding to
the different octane varieties.
There are four levels of a single explanatory variable.
•
-ÿh explanatory level has an associated level of
•
In a 1927-32 Western Electric Company study on the effect of lighting on worker productivity, productivity
increased with each increase in lighting but then also increased with every decrease in lighting. If it is
assumed that the workers knew a study was in progress, this is an example of
A1 the effect of a treatment unit
B. the placebo effect
C. the control group effect
)E lack of realism
• voluntary response bias.
10. Twenty men and 20 women with high blood pressure were subjects in an experiment to determine the
effectiveness of a new drug in lowering blood pressure. Ten of the 20 men and 10 of the 20 women were
chosen at random to receive the new drug. The remaining men and women received the placebo. The change in
blood pressure was measured for each subject. The design of this experiment is:
,) Randomized block, blocked by gender
B. Randomized block, blocked by drug
C. Randomized block, blocked by drug and gender
D. Completely randomized with one factor, drug
E. Completely randomized with one factor, gender
Free Response
11. An equipment firm is trying out three new types of grease in the transmissions of its front-end loaders. The
maintenance manager is interested in whether any of the greases reduce the time before the transmissions have
to be repaired• The company has 30 identical new front-end loaders to use in the test• How would you design the
experiment and in what way would you assign the front-end Ioaders?ÿ Be specific? Would you use a completeÿ/y
randomized design or a bT-'ÿ? How many factors are thereTÿHow many treatments? If it is-randomized . .
acteristic identifies the blocks? Explainyour decisions.
"
i
-
'
"
3
,Cl. ÿ//:k/
,
t
11. The Vita-Grow Company wants to test the relative effectiveness of 4 brands of fertilizer and to also control
for soil type• There are four types of soils: excellent, good, fair, and poor. The results are summarized
belOWl Is the experiment a cÿ,,r ..... , r ............ or ÿ How many factors are there? How
many treatments? If it is blocked, what are the blocks? "ÿ, 5(,d 1ÿ/ÿ
I(c,
Land Quality
Fertilizer 1
Excellent
Good
Fair
Poor
,.,
Fertilizer 2
Fertilizer 3
Fertilizer 4
xlÿ
xÿ2
x13
X14
Xzl
x22
x23
X24
x3ÿ
x3z
x33
X34
x42
x43
X4q
x41
--
Chapter 6 Review
If performances on AP Statistics tests are independent and the probability of passing an AP Statistics
test is 0.2, then the probability of passing three AP Statistics tests is:
(a) 0.6
(b) 0.2
(c) 0.04
dÿ.008
1
(e) 0
2). 45% of the WA upper school student body are male. 80% of the females love math, while only
....... 60°/o' of the maleslove math. What percentage of the student body love math?
(a) 70%
(b) 50%
(cÿ'1%
(d) 60%
(e) 100%
3) If 3 coins are tossed, what is the number of equally likely outcomes?
(a) 3
(c) 6
(d) 8
(e) 9
4) If P(A) = 0.23 and P(A and B) = 0.12 and P(A or B) = .34, find P(BC).
(a) 0.23
(b) 0152
(C) 0.11
ÿ'ÿ.77
(e) 0.48
k._./
5) How many possible 5-character code words are possible if the first two characters are letters and
the last three characters are numbers? (no character may be repeated)
(ÿ468000 (b) 82
(c) 676000 (d) 78
(e) Only a math genius can count that hight W
Free Response - Show your work.
6) In a recent survey of 100 lO-year olds, the following information was obtained:
53 liked McDonalds
12 liked both McDonalds and Burger King
6 liked all three
23 liked both McDonalds and Wendy's
4 liked only Burger King
24 liked Burger King
42 liked Wendy's
(a) Draw a Venn diagram illustrating this information.
(b) How many lO-year olds don't like any of these three?
_(c) What percentage of these/lO-year olds like Burger King and Wendy's?
,-
I/-{ °(a
If one of these lO-year old likes Wendy's, what is the probability that he likes Burger King?
ff
7)
If P(A) = 0.2 and P(B) = 0.3, find P(A or B) if:
(a)
A and B are independent.Lÿ
8)
A box contains four red tags numbered 1 through 4 and six blue tags numbered I through 6.
(b) A and B are disjoint.
(a) What is the sample space? Lÿtÿ ÿ[ÿ/ÿ(1 ÿÿl ÿ ÿÿ ÿ-,,ÿ
(b) Find the following probabilities:
P(red)
P(odd)
P(Red or Even)
P(Blue or even)
P(Even I Blue)
P(Not Red nor Even)
¢
.
9) You work at Circuit City. You track your customer's buying habits. Let event A={buying a DVR) and
event B={buying recordable DVD's}. If the following probabilities are given:
P( buying a DVR) = .6
P( buying recordable DVD's) = .7
P( Buying a DVR and recordable DVD's) = .36
Determine if events A and B are independent.
10) Refer to the data in this chart.
Degrees Earned by Gender
Female
Male
Total
Bachelor
Master's
616
194
30
16
856
529
1145
171
365
44
74
26
42
770
1626
Calculate the following probabilities:
(a) P(Bachelor's),i[ ÿ?ÿ_z,,ÿ
(b) P(Female I Doctorate)(ÿ.j,.
(c)
P(Male or Professional)
Professional Doctorate Total
11) When two numbered cubes are rolled, find the following probabilities:
Ca)
Rolling a sum of 7 qÿ/'ÿ-.
Cb)
Rolling a sum greater than 10 "ÿlÿ
Rolling a sum of 13
Rolling a sum less than 13
Rolling a sum less than 3 or greater than 10 ÿ6
(c)
Cd)
Ce)
12) The probability that an engine will not start is 0.04. A rocket has four independent engines. What
is the probability that at least one of the engines does not start?
a) .8154
b) .0O006
.1507
d) .0354
e) .0015
13) The probability that thunderstorms are in the area near DFW airport and that planes will land on
time is 0.56. If there are thunderstorms in the area of DFW, the probability that the plane lands
on time is 0180. What is the probability that there are thunderstorms in the area of DFW?
.448
c) 1.429
d) 1.36
e) cannot be calculated
14) Which of the following statements is not true?
a) In calculating permutations, the order in which the events occur does matter.
b)
A chance experiment is any activity or situation in which there is uncertainty concerning
which of two or more possible outcomes will result.
Two events are disjoint if they cannot occur simultaneously.
In order to calculate the compound event "or", the events must be independent.
e)
The probabilities of complementary events are always equal to one.
15) If a peanut M&M is chosen at random, the chances of it being a particular color are shown in the
following table.
Color Brown Red Yellow Green Orange
Blue
Probability .3
.2
.2
.2
.1
?
The probability of randomly drawing a blue peanut M&M is
a) 1.0
.1
J
.2
.3
According to this distribution it s ÿm
to draw a blue M&M.
16) Which of the following are true?
"buying
The event
TI calculator"
is considered a simple event.
a
b)
c)
If two events, A and B, are mutually exclusive, then P(A and B) = P(A) X P(B).
The probability of the union of two events is the sum of the probabilities of those events.
d)
The sum of the probabilities of events in a sample space can be any number between 0 and 1.
0
The probability that an event happens is equal to 1 minus the probability that the event does
not happen
17) The chances that you will be ticketed for illegal parking on campus on any given day is about 1/3.
During the last nine days, you have illegally parked every day and have NOT been ticketed (you lucky
person)! Today, on the 10th day, you again decide to park illegally. The chances that you will be caught
are:
a)
equal to 9/10 since you were not caught in the last nine days.
b)
greater than 1/3 since you were not caught in the last nine days.
less than 1/3 since you were not caught in the last nine days.
still equal to 1/3 since each day is independent of the other days.
e)
equal to 1/10 since you were not caught in the last nine days.
18) In one card game, three-card hands are dealt. What is the probability that the hand of three
Kings will be dealt?
a) .0129
b) 10139
c) 0
.0002
e) cannot be determined from the information given
19) A combination lock has a three-digit combination. If the digits (0-9) can be repeated, how many
different combinations are possible?
a) 120
b) 720
cÿ I000
d) 729
e) 504
20) Identify why this assignment of probabilities cannot be legitimate: P(A) = .4, P(B) = .3, P(A and B) =
.5.
O
b)
c)
P(A and B) cannot be greater than either P(A) or P(B).
A and B are not given as mutually exclusive events.
A and B are not given as independent events.
d)
P(AIB) is not known.
e) The assignment is leg!timate.
21) If the P(A) = .3, P(A or B) = .65, and events A.ÿ.& B are independent, find the P(B).
I
a) .8
b) .35
c) .15
"(dÿ5
Free Response
1) A fair coin is tossed six times, resulting in 6 heads being thrown. What is the probability that a
head will be thrown on the seventh toss? Explain.
2) In some states license plates consist of 4 letters followed by 2 or 3 digits. How many license plates
are possible if letters and digits can repeat?
3) Doc Worker is a regular customer at the Waterfront Coffee Shop. The manager has figured that
Doc°s probability of ordering ham is 0.5 and of ordering eggs is 0.85. Assuming that Doc orders food
independently of each other, what is the probability of the following?
a) He orders ham but not eggs.
,G'7
b) He orders at least one of the two.
Chapter 7 Review
A
1. Suppose the average height of policemen is 71 inches with a standard deviation of 4 inches, while 1
the average for policewoman is 66 inches with a standard deviation of 3 inches. If a committee looks
at all ways of pairing up one male with one female officer, what will be the mean and standard deviation
for the difference in heights for the set of possible partners?
(a) Mean of 5 inches with a standard deviation of 1 inch.
(b) Mean of 5 inches with a standard deviation of 3.5 inches.
Mean of 5 inches with a standard deviation of 5 inches.
(d) Mean of 68.5 inches with a standard deviation of 1 inch.
(e) Mean of 68.5 inches with a standard deviation of 3.5 inches.
2. Which of the following are true statements?
I.
By the law of large numbers, the mean of a random variable will get closer and closer to a
specific value.
II.
The standard deviation of a random variable is never negative.
III.
The standard deviation of a random variable is 0 only if the random variable takes a lone
single value.
(a) I and II
/
(b)I and III
(c) II and III
¢o) None of these gives a correct response.
L
dÿI, II and III
3. Which of the following is not true concerning discrete probability distribution?
(a) The probability of any specific value is between 0 and 1, inclusive.
)(b) The mean of the distribution is between the smallest and largest value in the distribution.
(c) The sum of all probabilities is 1.
The standard deviation of the distribution is between -1 and 1.
(e) The distribution may be displayed using a probability histogram.
4. AP Statistics test scores on Random Variables are described by the following probability
distribution.
Score
40
50
60
70
80
.2
.3
.3
.1
P(Score) .1
(a) Determine the mean and variance of the Scores.
(b) The teacher, in yet another act of benevolence, decides to scale the scores so his students will not
be denied admission to the college of their choice. He decides the actual grades will become: Grade
= 1.5 * Score - 20.
(i) Determine the mean and variance of the Grades.
(ii) Which Score(s), if any, did not increase?
5. In the game roulette, there are 18 black numbers, 18 red numbers, and 2 green numbers. If you bet
$1 on a color and win, you receive $1. In this game, you will not choose green as a color.
Consider your "gain" to be +$1 if you win and -$1 if you lose.
a) How much would you expect to gain on each play?
b)
/
If you bet on a color 100 times, how much would you expect to gain?