AP Statistics
Chapters 14-17
Review
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Class period______
WRITE ANSWERS AS DECIMALS WITH THREE SIGNIFICANT DIGITS.
1. Know the difference between mutually exclusive/disjoint and independent.
Know the four requirements of a binomial distribution.
2. Compute the following.
a. P(a certain event)
b. P(an impossible event)
3. A drug is effective in an average of 70% of the trials. Find the probability that this drug will
be effective in a)all of eight separate and independent cases b)at least one of four cases.
4. A fund raising committee is to be selected from a group of 14 members, including nine
college graduates (4 are women) and five people who did not graduate from college (2 are
women).
a. If the chairperson is randomly selected, find the probability of getting a woman.
b. If the chairperson is randomly selected, find the probability of getting a man or a college
graduate.
c. If two members are randomly selected for a special project, find the probability that they are
both women.
d. At each meeting, one of the 14 members is randomly chosen to be secretary. Find the
probability that the first two secretaries are both men. (A person may be selected more than
once.)
5. A multiple choice test allows answers of a, b, c, d, and e for each question. A student answers
ten questions by making random guesses.
a. What is the probability that the first answer is correct?
b. Find P(all ten answers are wrong)
c. Find P(at least one correct answer)
6. A college professor has two teaching assistants who help work with students during labs. One
shows up 80% of the time while the other shows up 92% of the time. What is the probability that
the professor will have a teaching assistant in the lab today?
7. A fire alarm goes off 8% of the school days in a particular school. When it goes off, 3% of
the time there is a real fire. What proportion of the school days is there a real fire?
8. If forty-five percent of the seniors go out to lunch everyday, what is the probability of
randomly selecting 4 seniors who all go out to lunch everyday?
9. Canada has developed a new missile that hits its targets 60% of the time. If two
missiles are fired independently of each other at a target, what is the probability that
a) both missiles hit the target?
b. at least one missile hits the target?
10. A sample of pizza sales was recorded in the chart below.
Crust
thick
thin
Meat Lovers
28
16
Type of Pizza
Cheese
16
15
Supreme
18
24
a) What is the probability of randomly selecting a thin crust pizza?
b) What is the probability of randomly selecting a supreme pizza?
c) What is the probability of randomly selecting a thin crust given that it is a meat lovers
pizza?
d) Are buying a thick crust and buying a supreme pizza independent?
11. Sports Illustrated surveyed readers to see how they exercised to maintain fitness. Suppose
that the categories were A) play a sport, B) walk, and C) lift weights and also suppose that
25% lift weights
16% play a sport and walk
15% walk and lift weights
36% play a sport
57% walk
6% only lift weights
7% walk, play a sport, and lift weights
Sketch a Venn diagram and the probability that a randomly selected person:
a) does not lift weights, walk, or play a sport
b) only walks
c) plays a sport and lifts weights
12. A survey is conducted to determine whether any relationship exists between level of
education and location of residence. A random sample of 500 people produced the results given
in the accompanying table. Find the probability that a randomly selected person
a) lives in a rural area given that they have a college education
b) has a secondary education given that they live in the suburbs
Location of residence
Urban
Suburban
Rural
elementary
18
10
35
Education
secondary
68
118
58
college
111
69
13
13. A national study found that the average family spent $422 a month on groceries with a
standard deviation of $84. The average amount spent on housing was $1120 a month, with a
standard deviation of $212. The expected total a family spends on food and housing is 422 +
1120 = $1532. What is the standard deviation of the total if both expense distributions are
roughly normal? (from Bock test B)
14. An intelligence test has a mean of 150 and a standard deviation of 12. In order to qualify for
a gifted program a candidate’s score must be in the top 18%. Assuming a normal distribution,
find the minimum acceptable score to qualify for the gifted program.
15. A physical fitness researcher devises a test of strength and finds that the results are normally
distributed with a mean of 84.5 pounds and a standard deviation of 7.8 pounds.
a. If a subject is randomly selected and measured, find the probability of a score between 84.5
pounds and 90.0 pounds.
b. If a subject is randomly selected and measured, find the probability of a score between 75.0
pounds and 100.0 pounds.
c. If a subject is randomly selected and measured, find the probability of a score below 92.3
pounds.
d. If a subject is randomly selected and measured, find the probability of a score greater than 88.0
pounds.
e. If a subject is randomly selected and measured, find the probability of a score between 75.0
pounds and 80.0 pounds.
16. The test from question 14 is also used to place students in regular classes. Students must not
be lower than the bottom 20% to qualify for a regular program. Find the minimum acceptable
score for the regular program.
17. Bud and Lou were arguing about scores on the Ace Slap-Stick Comedy Test. These scores
are distributed normally with a mean of 50. They agreed that 10% of the population had scores of
60 or better (and they were correct on this). Bud also claimed that 10% of the population had
scores of 40 or below.
A) Bud is correct.
B) Bud is correct but only because each score point is worth one percentage point.
C) Bud is mistaken.
D) More information is necessary before a decision can be made.
18. Which of these random variables has a geometric model?
A) The number of cards of each suit in a 10 card hand.
B) The number of people we check until we find someone with green eyes.
C) The number of cars inspected until we find three with bad mufflers.
D) The number of Democrats among a group of 20 randomly chosen adults.
E) The number of aces among the top 10 cards in a well-shuffled deck.
19. Which of the random variables above is most likely to have a binomial model?
20 .A paranormal researcher is studying ESP and has developed a test consisting of 5
independent questions. Let x represent the number of questions answered correctly.
Number correct (x)
P(x)
a)
b)
c)
d)
e)
0
.028
1
2
.308
What is the probability that a person gets exactly 1 correct?
What is the probability that a person gets at least 3 correct?
What is the probability that a person does not get 1 correct?
What is the mean of the distribution?
What is the standard deviation of the distribution?
3
.317
4
.163
5
.033
21. A contractor has a 0.80 probability of making $70,000, a 0.15 probability of losing $20,000,
and a 0.05 probability of breaking even. What is the expected value?
22. Premature babies are those born more than three weeks early. Newsweek reports that 10% of
the live births in this country are premature. Suppose that 350 live births are randomly selected.
a. What is the probability that more than 50 births are premature?
b. What is the probability that exactly 40 births are premature?
c. What is the probability that not more than 25 births are premature?
d. How many babies would you expect to be born prematurely?
e. What is the standard deviation?
23. In a survey conducted for Business Week by Louis Harris & Associates, 1250 adults were
asked, “Bearing in mind that they are paid out of taxes, do you think public school teachers are
paid enough, too little, or too much?” Fifty-five percent of these adults said “too little.” Assume
that this percentage is true for the population of all adults. Find the probability that in a random
sample of 12 adults, exactly 9 will say “too little” in response to the question.
24. Home Electric sells extension cords in bulk at wholesale prices, as well as individually at
retail prices. Next year’s sales depend on market conditions, but executives use probability to
find estimates of sales for the coming year. The following tables are estimates for next year’s
sales.
Number sold
Probability
WHOLESALE SALES
2,000
5,000
0.5
0.2
10,000
0.2
RETAIL SALES
Number sold
500
1,000
Probability
0.4
0.5
15,000
0.1
1,200
0.1
What profit does Home Electric expect to make for the next year if the profit from each extension
cord sold is $7 at wholesale and $10 at retail?
25. Test 1 has a mean of 84 and a standard deviation of 7.3. Test 2 has a mean of 79 and a
standard deviation of 8.1. If Rudy scored an 88 and Test 1 and an 84 on Test 2, which test did he
score better on relative to the rest of the students?
26. For each of the following situations, indicate whether a binomial distribution is a reasonable
probability model for the random variable X. Give a reason if a binomial distribution is not
appropriate.
a) You observe the gender of the next 50 children born at a local hospital; X is thee number of
girls among them.
b) A couple decides to continue to have children until their first boy is born; X is the total
number of children the couple has.
c) You want to know what percent of married people believe that mothers of young children
should not be employed outside the home. You plan to interview 50 people, and for the sake of
convenience you decide to interview both the husband and the wife of 25 married couples. The
random variable X is the number among the 50 persons interviewed who think mothers should
not be employed.
27. Surveys indicate that 5% of the students who took the SATs had enrolled in an SAT prep
course. Thirty percent of the SAT prep students were admitted to their first choice college, as
were 20% of the other students. You overhear a classmate say he got into the college he wanted.
What is the probability he didn’t take an SAT prep course?
28. An ice cream stand reports that 12% of the cones they sell are “jumbo” size. You want to see
what a “jumbo” cone looks like, so you stand and watch the sales for a while.
a) What is the probability that the first jumbo cone is the fourth cone you see them sell?
b) What is the probability there is exactly one jumbo among the first 6 cones sold.
c) How many cones would you expect to see until you see a jumbo cone?
****************************Answers*************************************
1. see text
2a) 1 b) 0
3. a) .0576
4. a) 6/14 = .429
5. a) .2
6.
b) .992
b) 8/14 + 9/14 - 5/14 = 12/14 = .857 c) .165 d) .327
b) (4/5)10 = .107
1 - .016 = .984
7.
c) 1 - .107 = .893
.0024
10.a) .470 b) .359 c) .364
d) P(thick) = P(thick | supreme)
62 18

117 42
.53 ≠ .43
not independent
8.
.0410
9. a) .36
A
16
7
4
8
6
11. a) .17
b) .33
c) .11
B
33
9
C
17
b) .84
12. a) .0674
b) .599
13. $228.03
14. 161.04 or 161
15. a) 0.2611 b) 0.8655
16. 139.92 or 140
17. A
20. a) .151
b) .513
c) .849
d) 2.535
c) 0.8413
18. B
d) 0.3264
e) 0.1698
19. D
e) 1.115
21. $53,000
22. a) 0.00426 (using binomcdf)) b) .0457
23. 0.0923
c) 0.0405 (using binomcdf)
d) 35 e) 5.612
24. $46,700
25. Test 2 (use z-scores to compare results)
26.a) Yes, a binomial distribution is appropriate
b) No, n is random and the distribution is geometric
c) No, trials are not independent; spouses influence each other and chose to be spouses
possibly based on similar opinions
27. 0.93
28. a) .08
b) .38
c) 8 or 9 (8.333)