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I Part Three: AP Statistics Review
190 J Chapter 12
REVIEW QUESTIONS
1. Based on concerns over the eating habits and fitness level of school-aged children, the
School Board of a large district decided to offer healthy choices in the school cafeterias.
They randomly selected students from all grade levels and provided them with proposed
menus for the healthier lunches. Students were asked if they would purchase these mnches.
The results of the survey are summarized in the table below by grade level.
K-5
6-8
9-12
Yes
6231
5964
3493
No
HE3I3
Total
1912
7876
What is the probability that a high school student selected at random would not plan
to purchase the proposed healthier lunches?
(A) .1672
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(D) .5007
(E) .9447
2. According to a recent national survey'of college students, 55% admitted to having
cheated at some time during the last year, what is the probability that for two
randomly selected college students, one or the other would have cheated during the
past
year?
.
(A) .5500
.7975
(C) .3025
(D) .2475
'(E) .2025
3art ihree: AP Statistics Review i
Probability 191
3. Given two events, A and B, if P(A) = .37, P(B) = .41, and the P(A or 3) = .75, then the
two
events
are
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(B)
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exclusive
but
not
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(C) mutually exclusive and inaependent ')
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or
mutually
exclusive.
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4. Security procedures at the U.S. Capitol require that all bags—meaning briefcases,
backpacks, shopping bags, any carrying bag and purses—must be screened. Currently,
it is reported that ninety-five percent of all bags that contain illegal items trigger the
alarm. Twelve percent of the bags that do not contain illegal items trigger the alarm.
If 3 out of every 1000 bags entering the Capitol contain an illegal item, what is the
probability that a big that triggers the alarm will contain an illegal item?
(B) .0029
(C) .9500
(D) .1140
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Part ihree: 192 Chapter 12
5. Suppose your teacher's stash of calculators contains 3 defective calculators and 17 good
calculators. You select two calculators from the box for you and your friend to use on
the AP Statistics exam. What calculations would you use to determine the probability
that one of the calculators drawn will be defective?
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Free-Response Question
The United States Youth Soccer Association estimates that 2% of those youths who
play travel or select soccer, programs designed to develop soccer skills beyond a
recreational level, try out for their state's Olympic Development Program (ODP). Of
those who try out, 93% go on to play in college, while only 81% of those who don't
i i try out end up playing in college. Of those who try out for ODP and go on to play in
"''college, 5% receive some scholarship money to play. This is compared to 2% of those
who don't try out for ODP and go on to play in college.
(a) Ryan's coach has encouraged him to try out for ODP. Ryan wants to know the
chances of getting some money to play in college if he tries out. Determine the
probability that Ryan would get money to play in college if he tried out.
(b) If a college player is selected at random, what is the probability that he tried out
for ODP?
(c) Given that a college player chosen at random receives scholarship money to play,
what is the probability that the player did not try out for ODP?
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AP Statistics Test - Probability
Name
CJi_ 1. Which two events are most likely to be independent?
/^■n—• A) having a flat tire, and being late for school
B) getting an A in math, and getting an A in Physics
C) having a driver's license, and having blue eyes
D) having a car accident, and having 3 inches of snow today
E) being a senior, and leaving campus for lunch
2. Political analysts estimate the probability that Hillary Clinton will run for president in
2008 is 45%, and the probability that NY's Governor George Pataki will run as the Republican
candidate is 20%. If their political decisions are independent, then what is the probability that
only Hillary runs for president?
A)
9%
B)ll%
C)25%
XD)36%
E)45%
S^3. A survey of some AP Stats students recorded gender and
Lefty Righty Total
whether the student was left or right-handed. Results were
66
Boy
summarized in a table like the one shown. If it turned out that
Girl
54
handedness was independent of gender, how many of the AP Stat
Total
20
100
120
students were lefty girls?
A) 4 B)7 C)9 D)10 E) It cannot be determined
4. The city council has 6 men and 3 women. If we randomly choose two of them to co-chair a
committee, what is the probability these chairpersons are the same gender?
A)
4/9
B)l/2
C)5/9
D)
5/8
E)
7/8
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jumbo" cam looks like, so wtj stand and wat£h the sales for^while. Wh^rfis thq/
ility that the^irst jumbo cone i^Ehe fourth con2"you see them seH?
A) 8% ^ B)33% /^C)40% /D) 60% iBf93%
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_ 9. 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 hgrjojiave when she has finished all 200 tosses?
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B)105
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D ) 11 5
E)150
>110. 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 ) 1 5 D ) 1 3 7 E ) I t c a n n o t b e d e t e r m i n e d
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11. Police reports about the traffic accidents they investigated last year indicated that 40 % of
the accidents involved speeding, 25% involved alcohol, and 10% involved both risk factors,
a) What is the probability that an accident involved neither alcohol nor speed?
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b) Do these two risk factors appear to be independent? Explain.
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12. Surveys indicate that 5 % of the students who took the SATs had enrolled in an SAT prep
course. 30% 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?
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13. A large corporation sponsors bowling leagues for its employees. The mean score for men
was 154 pins with a standard deviation of 9 pins, while the women had mean score 144 pins and
standard deviation 12 pins. At the end of the season the league holds a tournament that randomly
pairs men and women as opponents in the first round.
a) On average, how much do you expect the man to win by? [O
b) Estimate the standard deviation of the differences in the competitor's scores.
ISc) What assumption did you make in determining the standard deviation?
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16.
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.
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3
1
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b) Find the mean of the total.
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c) Find the standard deviation of the total.
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17. Suppose you use the two dice from #16 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.
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