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AP Statistics - Exam Review
You will be tested on these main topics on the Wednesday after Spring Break:
 Probability (independent events, dependent events, conditional probability, basic probability,
Venn Diagrams, union/intersection/complement)
 Random Variables (finding the expected value, finding the variance and standard deviation,
applying the rules)
 Binomial and Geometric Probability Models (identifying and understanding when to use a pdf
and when to use a cdf)
 Sampling distributions (for means, for proportions, estimating the normal distribution, the
Central Limit Theorem, the Law of Large numbers, all assumptions and conditions that need
to be met, and all related topics)
You need to look over your study guides and notes on these topics. This will be a big test and the study
guides and notes will help prepare you.
Questions:
Use the table for questions 1-4. The table below shows the results of a hypothetical survey on participation
in sports activities by men and women. Those surveyed answered yes to activities they had done at least
twice in the previous 12 months. Assume that the sample is representative of the overall population.
Men
Women
Total
109,059
115,588
Aerobic Exercising
3,717
19,535
Baseball
12,603
2,974
Hunting
18,512
2,343
Softball
11,535
8,541
Exercise Walking
25,146
46,286
1.
If you randomly select one man, what’s the probability that he hunts, expressed as a percentage?
A. 0.1697
B. 16.97%
C. 16.02%
D. 589.13%
E. 8.24%
2.
If you randomly select one woman, what’s the probability that she does aerobics?
A. 0.034
B. 0.169
C. 0.201
D. 0.087
E. 5.917
3.
If you randomly select one man, what’s the probability that he doesn’t do exercise walking?
A. 0.231
B. 1.300
C. 0.400
D. 0.660
E. 0.769
4.
If you randomly select one person from the study, what would be the probability that he or she plays
baseball for exercise, expressed as a percentage?
A. 11.56%
B. 2.57%
C. 6.93%
D. 7.07%
E. 3.47%
5.
Fred is a weightlifter who can lift 800 pounds on 45% of his attempts. Which of these expressions
represents the probability Fred will make 30 lifts out of 60?
A. N(60, 0.45, 30) B. B(60, 0.45, 30)
C. B(30, 0.45, 60)
D. B(30, 0.80, 60) E. N(30, 0.80, 60)
Suppose you roll a six-sided die 10 times. What’s the probability of getting three fives in those 10
rolls?
A. 0.60
B. 0.30
C. 0.155
D. 0.000618
E. 0.930
6.
7.
A.
B.
C.
D.
E.
8.
A.
B.
C.
D.
E.
If you roll a six-sided die 10 times, what’s P(x  3)?
1 – binomcdf(10, 1/6, 2)
1 – binomcdf(10, 1/6, 3)
3
7
4
6
9
1
10   1   5  10   1   5 
10   1   5 
              ...      
3  6   6   4  6   6 
9  6   6 
P(X=3) + P(X=4) + P(X=5) + P(X=6) + P(X=7) + P(X=8) + P(X=9) + P(X=10)
1 – binomcdf(10, 1/6, 4)
Under what conditions can you use a normal distribution to approximate the binomial distribution?
np  10 and n(1  p)  10
n  10
p = 0.5
You can’t. They are different distributions.
When you use the continuity correction.
9.
In a binomial distribution with sample size n = 65, and the probability of success p = 0.8, what would
the approximate mean of the distribution be?
A. 52
B. 65
C. 10.4
D. 3.22
E. 0.8
10.
In a binomial distribution with n = 140 and p = 0.62, what is the expected standard deviation of the
distribution, to the nearest hundredth?
A. 32.98
B. 0.04
C. 86.80
D. 5.74
E. 0.62
11.
You flip two coins. What is the probability of getting at least two heads?
A. 1/8
B. 5/8
C. 3/8
D. 1/4
E. 11/16
12.
One card is randomly selected from a standard 52-card deck. Find the probability that the card is an
ace or a black card.
A. 1/26
B. 1/13
C. 7/13
D. 15/26
E. 1/2
13.
Which of the following are true?
I.
If events A and B are independent, P( A or B)  P( A) P( B)
II.
If events A and B are independent, P( A)  P( A | B)
III.
If events A and B are disjoint, P( A or B)  P( A)  P( B)  P( A  B)
A. I only
B. II only
C. III only
D. I and II only
For questions 14 and 15, refer to the table below.
A
0.28
D
0.31
E
0.06
F
0.65
Total
B
0.10
0.16
0.04
0.30
C
0.02
0.03
0.00
0.05
E. I and III only
Total
0.40
0.50
0.10
1.00
14.
If one individual is drawn at random from this population, find P(A|D).
A. 0.28
B. 0.65
C. 0.40
D. 0.431
E. 0.70
15.
If one individual is drawn at random from this population, find P(D|A).
A. 0.28
B. 0.65
C. 0.40
D. 0.431
E. 0.70
16.
The following table is for a discrete probability distribution.
x
7
3
9
p
0.05
0.10
0.15
What number is missing?
A. 0.45
B. 1
C. 0.60
D. 0.20
11
Which of the following examples would constitute a discrete random variable?
I.
Total number of points scored in a football game.
II.
Height of the ocean’s tide at a given location.
III.
Number of near collisions of aircraft in a year.
A. I and II
B. I and III
C. I only
D. II only
15
0.25
E. 0.55
17.
E. I, II, and III
You’ve taken a random sample of beaches in the United States and measured their lengths. A
hypothetical probability distribution for beach length is represented in the table below. What’s the
probability of a randomly selected beach having a length of 12 miles?
X (length)
0 – 3 miles
3 – 6 miles
6 – 9 miles
9 – 12 miles
12 – 15 miles
P(X)
0.05
0.15
0.25
0.35
0.10
A. 0.35
B. 0.10
C. 0
D. 0.45
E. None of these.
18.
19.
Consider the following sample space for a random experiment: {1, 2, 3, 4, 5, 6, 7, 8}. Event A is
composed of the simple events {1, 3, 6, 8}. What is the complement of A?
A. {1, 3, 6, 8}
B. {1, 2, 3, 6, 7, 8} C. {1, 2, 3, 8}
D. {2, 4, 6, 7}
E. {2, 4, 5, 7}
For questions 20 and 21, use the table below.
x
-1
1
P(X)
25/36
10/36
20.
What is the expected value of X?
A. –5/36
B. 1
C. 1.93
21.
What is the variance of X?
A. –5/36
B. 1.93
C. 0
10
1/36
D. 5/36
E. 45/36
D. 3.73
E. 4.12
Use this information to answer questions 22 and 23. Given random variable X has 12 values with a mean of
8 and a standard deviation of 3. Random variable Y also has 12 values, but it has a mean of 11 and a
standard deviation of 2. A new random variable Z is created as follows: Z = 2X +3Y.
22.
What is the mean of Z?
A. 24
B. 12
C. 49
D. 60
E. Not enough info
23.
What is the standard deviation of Z?
A. 24
B. 72
C. 49
D. 60
E. Not enough info
In questions 24 and 25, refer to the following variables: consider two discrete, independent, random
variables X and Y with  x =3,  x2  1 ,  y =5,  y2  1.3 .
24.
A. 9
Find  32 6 X .
B. 6
25.
Find  X  Y and  X2 Y .
A. 8, 2.14
B. 15, 1.3
C. 8, 1.52
C. 39
D. 15, 2.3
D. 36
E. 81
E. The mean is 8, but sigma cannot be found
26.
When rolling a 6-sided die, what’s the probability of having to roll 6 times before you get a 4?
A. 0.167
B. 1
C. 0.067
D. 0.665
E. 0.000107
If you roll two dice, what’s the probability of rolling a seven (the numbers on the dice add up to 7) on
or before the eighth roll?
A. 0.767
B. 0.083
C. 0.47
D. 0.049
E. 0.045
27.
28.
What are the mean and the standard deviation of a sampling distribution consisting of samples of size
16? These samples were drawn from a population whose mean is 25 and standard deviation is 5.
A. 25, 1.25
B. 5, 5
C. 25, 5
D. 5, 1.25
E. 25, 5
What’s the probability of a sample of 10 students getting an average score of 510 or more on a
standardized test if the test’s scores are normally distributed with a mean of 505 and a standard
deviation of 50?
A. 0.4601
B. 0.6241
C. 0.1587
D. 0.3759
E. Cannot answer
29.
30.
Samples of size 49 are drawn from a distribution that is highly skewed to the right with a mean of 70
and a standard deviation of 14. What’s the probability of getting a sample mean between 71 and 73?
A. 0.0563
B. 0.00023
C. 0.2417
D. 0
E. Cannot answer
If you flip two coins simultaneously, what’s the probability you’ll have to flip them four times before
the first occurrence of two heads?
A. 0.25
B. 0.11
C. 0.683
D. 0.188
E. 0.14
31.
32.
Which of the following are true of all sampling distributions?
I.  x   ,  x 

.
n
II. It is a probability distribution of a statistic.
III. All samples must be the same size.
A. I only
B. II only
C. III only
D. I and II only
E. II and III only
33.
You have an SRS of 300 students selected from over 100,000 college students. Of your sample, 35%
said they had fallen asleep in their English class at least once during the previous semester. The
mean and standard deviation of this statistic are:
A.  p  35,  p  0.000758
B.  p  105,  p  8.26
C.  p  105,  p  0.028
D.  p  .35,  p  0.028
E. You cannot answer because the sample size is not large enough relative to the population size.
34.
According to the manufacturer, the average proportion of red candies in a package is 20%. An 8
ounce package contains about 250 candies. What is the probability that a randomly selected 8 ounce
bag contains less than 45 red candies?
A. 0.788
B. 0.317
C. 0.212
D. 0.155
E. None of these
About 25% of all dogs live more than 10 years. Out of a random sample of 80 dogs, what’s the
probability that between 15 and 20 dogs will live more than 10 years?
A. 0.40
B. 0.09646
C. 0.02
D. 0.50
E. Cannot do
35.
36.
A bag of candy has equal numbers of candies in eight colors: blue, red, brown, green, yellow, orange,
pink, and black. If you eat them one by one, what’s the probability of getting your first red candy on
or before the fifth pick?
A. 0.547
B. 0.875
C. 0.607
D. 0.5512
E. 0.487
37.
The standard deviation of SAT scores is 100 points. A researcher decides to take a sample of 500
student scores to estimate the mean score of students in your state. What is the standard deviation of
the sample mean?
A. 0.2
B. 4.47
C. 5
D. 100
E. Cannot determine
Extended Response Questions:
1.
A random variable X has the following probability distribution:
x
1
2
3
P(X)
0.087
0.453
4
0.234
5
0.095
a) What is P(2)?
b) Construct a probability histogram of the distribution.
2.
You have a bag of 30 candies: 10 red, 5 green, 5 brown, 8 yellow, 1 orange, 1 blue. You randomly
select two candies from the bag. You’re interested in the random variable X for the number of
yellow candies chosen from the bag. What is P(X)?
3.
You have a standard deck of cards.
a) What is the probability of randomly drawing a face card (Jack, Queen, King, or Ace) from this
deck?
b) Starting with the original deck, what’s the probability of randomly selecting a black king?
c) Now remove all the face cards from the deck. At this point, what’s the probability of randomly
selecting a diamond from the deck?
d) You leave these 36 cards lying on a table in your house. You go back to your cards and
realize that your dog ate some of the cards. For some strange reason he really likes the cards in
the clubs suit. You throw away the chewed cards and randomly select a diamond from what’s
left of the deck. Would you expect the likelihood of selecting a diamond to increase, decrease, or
remain the same as the previous draw?
4.
In a sample of 5,000 patients we find that 220 have kidney disease, 780 have cancer, 1,093 have heart
disease, and 1,290 have arthritis.
a) What is the probability of selecting an individual with kidney disease?
b) What is the probability of selecting an individual with cancer?
c) What is the probability of selecting an individual with heart disease?
d) What is the probability of selecting an individual with arthritis?
e) Dr. Jones has his own random sample of 75 patients. What’s the expected number of patients with
each of these four medical conditions?
5.