Download Chapter 5 Review - Spring

Chapter 5 Review
AP Statistics
Name __________________________
Date___________________Per______
___ 1. A survey taken in 2009 indicated that approximately 86% of teens own some form of an IPod. What is the
probability that of three randomly selected teens, at least one owns an IPod?
a. 0.27%
b. 28.7%
c. 63.6%
d. 86%
e. 99.7%
___ 2. Which two of these events are most likely to be independent?
a. Getting an A in AP English and scoring over 600 on the SAT verbal test
b. Eating a Big Mac every day and having higher than average cholesterol
c. Being a binge drinker and flunking out of college
d. Having blue eyes and enjoying gym class
e. Owning a laptop and being a college student
___ 3. If P(B)=0.4 and P(A
a. 0.475
b. 0.525
c. 0.600
d. 0.084
e. Not possible
B)=0.21, then find P(A) if A and B are independent.
___ 4. Your classmate plans to toss a fair quarter 500 times. You watch the first 50 tosses and are surprised that
he got 40 tails. You receive a call on your cell phone and miss the remainder of the tosses. How many tails do you
expect him to have when he has finished all 500 tosses?
a. 200
b. 225
c. 250
d. 265
e. 400
___ 5. Computer voice recognition software is getting better. Some companies claim that their software correctly
recognizes 98% of all words spoken by a trained user. To simulate recognizing a single word when the probability
of being correct is 0.98, let two digits simulate one word; 00 to 97 mean “correct.” The program recognizes words
(or not) independently. To simulate the program’s performance on 10 words, use these random digits:
60970 70024 17868 29843 61790 90656 87964
The number of words recognized correctly out of the 10 is
a. 10
b. 9
c. 8
d. 7
e. 6
Questions #6 to 8 refer to the following setting: One thousand students at a city high school were classified
according to both GPA and whether or not they consistently skipped classes. The two-way table below summarizes
the data. Suppose that we choose a student from the school at random.
___ 6. What is the probability that a student has a GPA under 2.0?
a. 0.227
b. 0.255
c. 0.450
d. 0.475
e. 0.506
___ 7. What is the probability that a student has a GPA under 2.0 or has skipped many classes?
a. 0.080
b. 0.281
c. 0.285
d. 0.365
e. 0.727
___ 8. What is the probability that a student has a GPA under 2.0 given that he or she has skipped many classes?
a. 0.080
b. 0.281
c. 0.285
d. 0.314
e. 0.727
___ 9. Choose an American adult at random. The probability that you choose a woman is 0.52. The probability
that the person you choose has never married is 0.25. The probability that you choose a woman who has never
married is 0.11. The probability that the person you choose is either a woman or has never been married (or
both) is therefore about
a.
b.
c.
d.
e.
0.77
0.66
0.44
0.38
0.13
___ 10. A deck of playing cards has 52 cards, of which 12 are face cards. If you shuffle the deck well and turn over
the top 3 cards, one after the other, what’s the probability that all 3 are face cards?
a.
b.
c.
d.
e.
0.001
0.005
0.010
0.012
0.02
11. A survey was run in a high school about vacations which found that 22% of students have taken a cruise during
a school year, 28% have gone to Disney during a school year, and 13% have taken both trips during a school year.
a. Sketch a Venn diagram or two-way table that summarizes the probabilities above.
b. Find the probability that a randomly selected student has only taken a cruise during instructional time.
c. Find the probability that a randomly selected student has taken a cruise or gone to Disney during school.
d. Find the probability that a randomly selected student has gone to Disney but has not taken a cruise during
the school year.
e. Find the probability that a randomly selected student has not gone to Disney and has not taken a cruise
during the school year
f.
Are “taking a cruise” and “going to Disney” disjoint events? Explain (in context).
g. Are “taking a cruise” and “going to Disney” independent events? Explain (in context).
12. Suppose that 23% of adults smoke cigarettes. It’s known that 57% of smokers develop a certain lung
condition by the age of 60. Unfortunately, 13% of nonsmokers also develop the same condition.
a. What is the probability that an adult develops the lung condition by age 60?
b. Suppose an adult male is admitted to the hospital with that lung condition. What is the probability that
he is a nonsmoker?
13. The “random walk” theory of stock prices holds that price movements in disjoint time periods are
independent of each other. Suppose that we record only whether the price is up or down each year, and that the
probability that our portfolio rises in price in any one year is 0.65.
a. What is the probability that our portfolio goes up for three consecutive years?
b. What is the probability that the portfolio’s value moves in the same direction (either up or down) for
three consecutive years?
c. What is the probability that the portfolio’s value moves down in at least one of the next 5 years?
d. Describe what the Law of Large Numbers says in the context of this probability.
14. The Mars candy company starts a marketing campaign that puts a plastic game piece in each bag of M&Ms.
25% of the pieces show the letter “M”, 10% show the symbol “&”, and the rest just say “Try again”. When you
collect a set of three symbols “M”, “&”, and “M” you can turn them in for a free bag of candy. About how many
bags will a consumer have to buy to get a free one? Use a simulation to find out.
a. Explain how you will use the random numbers listed below to conduct your simulation.
b. Carefully label your simulation for 2 trials.
c. State your conclusion.
15. From police records, it has been determined that 15% of drivers stopped for routine license checks are not
wearing seat belts. If a police officer stops 10 vehicles, how likely is it that two consecutive drivers won’t be
wearing their seat belts?
a. Describe the design of a simulation to estimate this probability. Explain clearly how you will use the partial table
of random digits below to carry out your simulation.
b. Carry out three repetitions of the simulation. Mark on or directly above the table to show your results.
30734 71571 83722 79712 25775 65178 07763 82928 31131 30196
64628 89126 91254 24090 25752 03091 39411 73146 06089 15630
42831 95113 43511 42082 15140 34733 68076 18292 69486 80468
c. Conclusion: