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AP STATISTICS
Unit IV Review
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1.
A fair coin has come up “heads” 10 times in a row. The probability that the coin will
come up heads on the next flip is
A) less than 50%, since “tails” is due to come up.
B) 50%.
C) greater than 50%, since it appears that we are in a streak of “heads.”
D) It cannot be determined.
2.
According to the National Telecommunication and Information Administration, 56.5% of
U.S. households owned a computer in 2001. What is the probability that of three
randomly selected U.S. households at least one owned a computer in 2001?
A) 18.0%
B) 43.5%
C) 56.5%
D) 82.0%
E) 91.8%
3.
According to the National Telecommunication and Information Administration, 50.5% of
U.S. households had Internet access in 2001. What is the probability that four randomly
selected U.S. households all had Internet access in 2001?
A) 6.5%
B) 12.6%
C) 49.5%
D) 50.5%
E) 93.5%
4.
Which of these has a Binomial model?
A) the number of people we survey until we find someone who has taken Statistics
B) the number of people we survey until we find two people who have taken Statistics
C) the number of people in a class of 25 who have taken Statistics
D) the number of aces in a five-card Poker hand
E) the number of sodas students drink per day
5.
Which of these has a Geometric model?
A) the number of people we survey until we find someone who has taken Statistics
B) the number of people we survey until we find two people who have taken Statistics
C) the number of people in a class of 25 who have taken Statistics
D) the number of aces in a five-card Poker hand
E) the number of sodas students drink per day
6.
Some marathons allow two runners to “split” the marathon by each running a half
marathon. Alice and Sharon plan to split a marathon. Alice’s half-marathon times
average 92 minutes with a standard deviation of 4 minutes, and Sharon’s half-marathon
times average 96 minutes with a standard deviation of 2 minutes. Assume that the
women’s half-marathon times are independent. The expected time for Alice and Sharon
to complete a full marathon is 92 +96=188 minutes. What is the standard deviation of
their total time?
A) 2 minutes
B) 4.5 minutes
C) 6 minutes
D) 20 minutes
E) It cannot be determined
7.
Insurance company records indicate that 12% of all teenage drivers have been ticketed
for speeding and 9% for going through a red light. If 4% have been ticketed for both,
what is the probability that a teenage driver has been issued a ticket for speeding but
not for running a red light?
A) 3%
B) 8%
C) 12%
D) 13%
E) 17%
8.
Which two events are most likely to be independent?
A) being a senior; going to homeroom
B) registering to vote; being left-handed
C) having a car accident; having a junior license
D) doing the Statistics homework; getting an A on the test
E) having 3 inches of snow in the morning; being on time for school
9.
A poll of 120 Ithacans found that 30 had visited the Museum of the Earth, and that 80
had been to Home Depot. If it appeared that going to Home Depot and going to the
Museum of the Earth were independent events, how many of those polled had been to
both ?
A) 10
B) 15
C) 20
D) 24
E) It cannot be determined.
10.
A friend of yours plans to toss a fair coin 200 times. You watch the first 40 tosses,
noticing that she got only 16 heads. But then you get bored and leave. If the coin is fair,
how many heads do you expect her to have when she has finished the 200 tosses?
A) 80
B) 92
C) 96
D) 100
E) 116
11.
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 (rent or mortgage)
was $1120 a month, with standard deviation $212. The expected total a family spends
on food and housing is 422+1120 = $1542. What is the standard deviation of the total?
A) $128
B) $148
C) $228
D) $295
E) It cannot be determined
12.
Which of these has a geometric model?
A) The number of black cards in a 10-card hand.
B) The colors of the cars in Wegman’s parking lot.
C) The number of hits a baseball player gets in 6 times at bat.
D) The number of cards drawn from a deck until we find all four aces.
E) The number of people we survey until we find someone who owns an iPod.
13.
Which of those choices listed in problem 12 is most likely to have a binomial model?
14.
Pepsi is running a sales promotion in which 12% of all bottles have a “FREE” logo under
the cap. What is the probability that you find two free ones in a 6-pack?
A) 1%
B) 11%
C) 13%
D) 23%
E) 97%
15.
A supermarket claims that their checkout scanners correctly price 99.8% of the items
sold. How many items would you expect to buy, on average, to find one that scans
incorrectly?
A) 2
B) 99.8
C) 200
D) 500
E) 998
16.
A survey of some AP Stats students recorded gender and whether the student was left
or righthanded. Results were summarized in a table like the one shown. If it turned out
that handedness was independent of gender, how many of the AP Stat students were
lefty girls?
A) 4
B) 7
C) 9
D) 10
E) It cannot be determined.
17.
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.
18.
Which of the random variables in #17 is most likely to have a binomial model?
19.
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.
What is the probability that the first jumbo cone is the fourth cone you see them sell?
A) 8%
B) 33%
C) 40%
D) 60%
E) 93%
20.
What is the probability there is exactly 1 jumbo among the first 6 cones sold by the ice
cream stand in #22?
A) 6%
B) 12%
C) 38%
D) 54%
E) 84%
21.
A friend of yours plans to toss a fair coin 200 times. You watch the first 20 tosses and
are surprised that she got 15 heads. But then you get bored and leave. How many
heads do you expect her to have when she has finished all 200 tosses?
A) 100
B) 105
C) 110
D) 115
E) 150
22.
On a physical fitness test middle school boys are awarded one point for each push-up
they can do, and a point for each sit-up. National results showed that boys average 18
pushups with a standard deviation of 4 push-ups, and 34 sit-ups with standard deviation
11. The mean of their combined (total) scores was therefore 18 + 34 = 52 points. What
is the standard deviation of their combined scores?
A) 5.3
B) 11.7
C) 15
D) 137
E) It cannot be determined
23.
Assume that 70% of teenagers who go to take the written drivers license test have
studied for the test. Of those who study for the test, 95% pass; of those who do not
study for the test, 60% pass. What is the probability that a teenager who passes the
written drivers license test did not study for the test?
24.
According to the National Health Survey, heights of adults may have a Normal model
with mean heights of 69.1” for men and 64.0” for women. The respective standard
deviations are 2.8” and 2.5.”
a.
Based on this information,
i.
how much taller are men than women, on average?
ii.
b.
what is the standard deviation for the difference in men’s and women’s
heights?
Assume that women date men without considering the height of the man (i.e.,
that the heights of the couple are independent). What is the probability that a
woman dates a man shorter than she is?
25.
26.
27.
28.
According to infoplease, 18.8% of the luxury cars manufactured in 2003 were silver. A
large car dealership typically sells 50 luxury cars a month.
a.
Explain why you think that the luxury car sales can be considered Bernoulli trials.
b.
What is the probability that the fifth luxury car sold is the first silver one?
c.
Let X represent the number of silver luxury cars sold in a typical month. What is
the probability model for X? Specify the model (name and parameters), and tell
the mean and standard deviation.
According to the Bureau of the Census, 68.0% of Americans owned their own homes in
2003. A local real estate office is curious as to whether a higher percentage of
Americans own their own homes in its area. The office selects a random sample of 200
people in the area to estimate the percentage of those people that own their own
homes.
a.
Verify that a Normal model is a useful approximation for the Binomial in this
situation.
b.
What is the probability that at least 140 people will report owning their own
home?
c.
Based on the sample, how many people would it take for you to be convinced
that a higher percentage of Americans owns their own homes in that area?
Explain.
Assume the heights of high school basketball players are normally distributed. For boys
the mean is 74 inches with a standard deviation of 4.5 inches, while girl players have a
mean height of 70 inches and standard deviation 3 inches. At a mixed 2-on-2
tournament teams are formed by randomly pairing boys with girls as teammates.
a.
On average, how much taller do you expect the boy to be?
b.
What will be the standard deviation of the difference in teammates’ heights?
c.
On what fraction of the teams would you expect the girl to be taller than the boy?
Two players compete against each other by rolling dice – not the traditional dice,
though. One face of Alphonso’s die has an 8 and the other five faces are all 2’s.
Bettina’s die has four 3’s and two 1’s on the six faces.
a.
They each roll their die, and the player with the highest score wins. Which player
has the advantage? Explain.
b.
If Alphonso wins, Bettina pays him $10. How much should he pay her if she wins
in order to make the game fair?
c.
They decide to change the rules. They’ll each roll, and the winner will collect the
number of dollars shown on his or her die. For example, If Alphonso rolls a 2 and
Bettina rolls a 3, he’ll pay her $3. Create a probability model for the amount
Alphonso wins.
29.
30.
31.
32.
d.
Find the expected value and standard deviation of Alphonso’s winnings at this
game.
e.
If they play this new game repeatedly which player has the advantage? Explain.
State public health officials claim that 18% of adults currently smoke cigarettes.
a.
We start selecting a few adults at random, asking each if he or she is a smoker.
Explain why these can be considered Bernoulli trials.
b.
How many people do you expect to have to ask in order to find a smoker?
c.
Let X represent the number of smokers among a randomly chosen sample of 30
adults. What is the probability model for X? Name the model (including its
parameters) and specify the mean and standard deviation of X.
d.
What is the probability that there are at least 8 smokers among our sample of 30
people?
Safety officials hope a public information campaign will increase the use of seatbelts
above the current 70% level. Their efforts include running radio and TV ads, putting up
billboards, having police officers appear on talk shows, and getting newspapers to
indicate whether people injured in accidents were belted in. After several months they
check the effectiveness of this campaign with a statewide survey of 560 randomly
chosen drivers. 407 of those drivers report that they wear a seatbelt.
a.
Verify that a Normal model is a good approximation for the binomial model in this
situation.
b.
Does the survey result suggest that the education/advertising campaign was
effective? Explain.
A game is played with 2 strange dice.
• The six faces of Die A show a 1 and five 3’s.
• Die B has four 2’s and two 6’s.
a.
Create a probability model for the total you get when you roll both dice.
b.
Find the mean of the total.
c.
Find the standard deviation of the total.
Suppose you use the two dice from #31 in a competition against another player. You
will roll one of the dice and your opponent will roll the other one. The winner is the
person who rolls the higher number. You get first choice of dice and want to win. Would
you pick Die A or Die B? Explain why.