Download AP Statistics Unit 4 Review Multiple Cho

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AP Statistics
Unit 4 Review
Multiple Choice:
1.
In a 1974 “Dear Abby” letter a woman lamented that she had just given birth to her eighth child, and all
were girls! Her doctor had assured her that the chance of the eighth child being a girl was only 1 in 100.
What was the real probability that the eighth child would be a girl?
a) 0.5
b) 0.0039
c) 0.001
d) 0.0000248 e) 4
2.
A deck of playing cards has 52 total cards of which 12 are face cards. What is the probability of
choosing 3 cards in a row without replacement and getting 3 face cards (approximately)?
a) 0.001
b) 0.005
c) 0.01
d) 0.02
e) 0.06
3.
The time it takes for students to complete a standardized exam is approximately normal with a mean of
60 minutes and a standard deviation of 15 minutes. Using the 68–95–99.7 rule, what percentage of
students will take over 75 minutes to complete the exam?
a) 68%.
b) 47.5%.
c) 32%.
d) 16%.
e) 5%
4.
Which of the following are true statements?
I.
The probability of an event is always at least 0 and at most 1.
II.
The probability that an event will happen is always 1 minus the probability that it won’t happen.
III.
If two events cannot occur simultaneously, the probability that at least one event will occur is the
sum of the respective probabilities of the two events.
a) I and II
b) I and III
c) II and III
d) I, II, and III
e) None of these
5.
A license plate consists of two letters of the alphabet, followed by three odd digits. A letter may be
repeated, but the three digits must be different. How many different license plates are there?
a) 39,000
b) 40,560
c) 52,440
d) 81,250
e) 84,500
6.
Given events A and B, where P(A c )  1 / 4 , the probability of the union of A and B equals 7/8, and the
probability of the intersection of events A and B equals 1/5. What is the value of P(B) ?
a) 13/40
b) 3/10
c) 7/25
d) 11/50
e) 3/20
7.
Suppose that for a certain Caribbean island in any 3-year period the probability of a major hurricane is
0.25, the probability of water damage is 0.44, and the probability of both a hurricane and water damage
is 0.22. What is the probability of water damage given that there is a hurricane?
a) 0.47
b) 0.50
c) 0.69
d) 0.88
e) 0.91
8.
There are two games involving flipping a coin. In the first game you win a prize if you can throw
between 45% and 55% heads. In the second game you win if you can throw more than 80% heads. For
each game would you rather flip the coin 30 times or 300 times?
a) 30 times for each game
b) 300 times for each game
c) 30 times for the first game and 300 times for the second
d) 300 times for the first game and 30 times for the second
9.
A sample of 150 people are checked to determine their blood type. The results show that 60 have
Type O, 40 have Type A, 30 have Type B, and the remaining individuals have Type AB. If one person
is randomly selected, what is the probability that this person has either Type A or Type AB blood?
a) 8/225
b) 2/25
c) 2/5
d) 3/5
e) 13/15
10.
Suppose that for any given year, the probabilities that the stock market declines, that women’s hemlines
are lower, and the both events occur are respectively, 0.4, 0.35, 0.3. Are the two events independent?
a) Yes, because  0.4  0.35   0.3
b) No, because  0.4  0.35   0.3
c) Yes, because 0.3  0.35  0.4
d) No, because 0.5  0.3  0.4   0.35
e) There is insufficient information to answer this question.
Free Response:
11.
Give two examples of disjoint events.
12.
A sample survey chooses a sample of households and measures their annual income and their savings.
Some events of interest are:
A=the household chosen has income at least $100,000
C=the household chosen has at least $50,000 in savings
Based on this sample survey, we estimate that P(A)  0.07 and P(C)  0.2
a)
We want to find the probability that a household either has income at least $100,000 or savings
at least $50,000. Explain why we do not have enough information to find this probability. What
additional information is needed?
b)
We want to find the probability that a household has income at least $100,000 and savings at
least $50,000. Explain why we do not have enough information to find this probability. What
additional information is needed?
13.
All human blood type can be “ABO-typed” as one of O, A, B, or AB, but the distribution of the types
varies a bit among groups of people. Here is the distribution of blood types for a randomly chosen
person in the United States:
Blood Type: U.S. Probability: 14.
O 0.45 A 0.40 B 0.11 AB ? a)
What is the probability of type AB blood in the United States?
b)
An individual with type B blood can safely receive transfusions only from persons with type B or
type O blood. What is the probability that the husband of a woman with type B blood is an
acceptable blood donor for her?
c)
What is the probability that in a randomly chosen couple the wife has type B blood and the
husband has type A?
d)
What is the probability that one of a randomly chosen couple has type A blood and the other has
type B?
e)
What is the probability that at least one of a randomly chosen couple has type O blood?
The distribution of blood types in China differs from the U.S. distribution given in the previous exercise:
Blood Type: China Probability: O 0.35 A 0.27 B 0.26 AB 0.12 Choose two people, one American and one Chinese at random, and independently of each other.
a)
What is the probability that both have type O blood?
b)
What is the probability that both have the same blood type?
15.
The owner of a bakery knows that the daily demand for a highly perishable cheesecake is as follows:
Number sold per day: Relative frequency: 0 0.05 1 0.15 2 0.25 3 0.25 4 0.20 5 0.10 a)
State the assumptions and assignments that should be used for this simulation.
b)
Use simulation to find the demand for the cheesecake on 30 consecutive business day.
c)
Suppose that it costs the baker $5 to produce a cheesecake, and that the unused cheesecakes must
be discarded at the end of the business day. Suppose also that the selling price of a cheesecake is
$13. Use simulation to estimate the number of cheesecakes that he should produce each day in
order to maximize his profit.
16.
A company retains a psychologist to assess whether job applicants are suited for assembly-line work.
The psychologist classifies applicants as A (well suited), B (marginal), or C (not suited). The company
is concerned about event D: an employee leaves the company within a year of being hired. Data on all
people hired in the past 5 years give these probabilities:
P(A) = 0.4 P(B) = 0.3 P(C) = 0.3 P(A and D) = 0.1 P(B and D) = 0.1 P(C and D) = 0.2 Sketch a Venn diagram of the events A, B, C, and D and mark on your diagram the probabilities of all
combinations of psychological assessment and leaving (or not) within a year. What is P(D), the
probability that an employee leaves within a year?
17.
Independence of events is not always obvious. Toss two balanced coins independently. The four
possible combinations of heads and tails in order each have probability 0.25. The events
A = head on the first toss
B = both tosses have the same outcome
may seem intuitively related. Show that P(B|A) = P(B), so that A and B are in fact independent.
18.
A school district has regularly administered a test to all first-graders, based on which a child is labeled
“exceptional” or “not exceptional.” On the basis of information other than scores on this test, some of
the children were placed in a special class for the gifted. Data collected to analyze the test showed that
80% of those who had succeeded in the special class had been labeled exceptional, 30% of those who
had not succeeded in the class had also been labeled exceptional, and that 75% of the children in the
special class had been successful. What is the probability that a child labeled exceptional on the basis of
the test will succeed in the special class?
19
Suppose there are 12 marbles in a bag, 8 red and 4 blue. You draw one marble from the bag and note its
color. You then draw a second marble without replacement.
a)
Draw the tree diagram for the sample space and the give the probability for each outcome of two
marbles.
b)
Determine the probability that both marbles drawn are same color.
20.
In the November 27, 1994 issue of Parade magazine, the “Ask Marilyn” section contained this question:
“Suppose a person was having two surgeries performed at the same time. If the chances of success for
surgery A are 85% and the chances of success for surgery B are 90%, what are the chances that both
would fail?” What do you think of Marilyn’s solution:  0.15  0.10   .015 or 1.5%?
Definitions:
21.
Vocabulary:
Trial Random Probability Independence Random phenomenon Sample space Tree diagram Replacement Event P(A) Complement A c Disjoint 22.
In statistics, what is meant by the term random?
23.
In statistics, what is meant by probability?
24.
What is probability theory?
25.
In statistics, what is meant by an independent trail?
26.
In statistics, what is a sample space?
27.
In statistics, what is an event?
28.
Explain why the probability of any event is a number between 0 and 1.
29.
What is the sum of the probabilities of all possible outcomes?
30.
Describe the probability that an event does not occur?
31.
What is meant by the complement of an event?
32.
When are two events considered disjoint?
33.
What is the probability of the union of two disjoint events?
Venn Diagram Union (or) Intersection (and) Joint event Joint probability Conditional probability 34.
Explain why the probability of getting heads when flipping a coin is 50%?
35.
What is the Multiplication Rule for independent events?
36.
Can disjoint events be independent?
37.
If two events A and B are independent, what must be true about A c and Bc ?
38.
What is meant by the union of two or more events? Draw a diagram.
39.
State the addition rule for disjoint events.
40.
State the general addition rule for unions of two events.
41.
Explain the difference between the rules in #35 and #36.
42.
What is meant by joint probability?
43.
What is meant by conditional probability?
44.
State the general multiplication rule.
45.
How is the general multiplication rule different than the multiplication rule for independent events?
46.
State the formula for finding conditional probability.
47.
What is meant by the intersection of two or more events? Draw a diagram.
48.
Explain the difference between the union and the intersection of two or more events.
49.
State the formula used to determine if two events are independent.
Selected Answers
1. A
2. C
3. D
4. D
5. B
6. A
7. D
8. D
9. A
10. B
11. D
13. a) 0.04
b) 0.56
c) 0.044
d) 0.088
e) 0.6975
14. a) 0.1575
b) 0.2989
16. 0.4
18. P(success | exceptional) = 60/67.5 = .8889
19. b) 0.5151