Download AP MC Discrete Distributions

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AP Statistics - AP Review - Discrete Distributions
1) Assume that the probability that a baseball player will get a hit in
any one at-bat is .250. Which expression will yield the probability that
his first hit will next occur on his 5th at-bat?
5 
a)  .250 4 .750 1
4
b) .7504 .250
c) .250 4 .750 
d)  .250 1 .750 4
1
 
5
 
2) Binomial and geometric probability situations share all of the
following conditions except one. Identify the choice not shared.
a) The probability of success on each trial is the same.
b) There are only two outcomes.
c) The focus of the problem is the number of successes in a given
number of trials.
d) The probability of a success equals 1 minus the probability of a
failure.
e) All of these are shared by binomial and geometric situations.
3) Which of the following is not true of discrete probability
distributions?
a) The sum of the probabilities is 1.
b) The graph of the distribution exhibits symmetry.
c) The value of the standard deviation can be less than, equal to, or
greater than the value of the mean.
d) Each of the probability in the distribution must be greater than or
equal to 0.
e) All of these are true statements.
4) If three people, Joe, Betsy, and Sue, play a game in which Joe has a
25% chance or winning and Betsy has a 40% chance of winning, what
is the probability that Sue will win? (There is only one winner & no
ties.)
a) 25%
c) 65%
e) Cannot be determined
b) 40%
d) 35%
Use the following to answer questions 5 & 6: A company claims that
the number of defective items manufactured during each run of
making 100 of their products is independent of the number from other
runs and that the proportion of defectives is not more than 4%.
Assume that the proportion of defectives for each run is .04.
5) What is the probability that there will be no defectives on the next
run?
a) .034
c) .017
e) None of these.
b) .051
d) .0085
6) The distribution of the number of defectives in each run of the
manufacturing process has an expected value of 4 and a standard error
of 1.96. Which of the following is a correct interpretation of these
values?
a) There is a probability of .95 that the number of defectives will be
within 3.92 of 4.
b) There is a .0196 probability that the number of defectives will equal
4.
c) The distribution is symmetric and mound-shaped with the center at
4.
d) The rule of thumb dealing with percentages of data with 1, 2, and 3
standard deviations of the mean cannot be applied since this
distribution could be severely skewed.
e) None of these is a correct interpretation.
7) Which of the following statements is true?
a) Both the Poisson and geometric distributions are finite.
b) Both the Poisson and binomial distributions become more
symmetrical as the average or probability of success increases.
c) Both the Poisson and binomial distributions have random variables
that begin with X = 0.
d) Both geometric and binomial distributions shift to the right as the
probability of success increases.
e) Both the geometric and binomial distributions are infinite.
8) A knife thrower estimates that he can hit his target 95% of the time.
Assuming that each of his throws is independent, which of the
following probability statements is correct?
6
2
4
a) P(4 hits in his next 6 throws) =  .05 .95
 4
b) P(4 hits in his next 6 throws) = .05 .95
6
4
2
c) P(4 hits in his next 6 throws) =  .05 .95
 4
2
4
d) P(4 hits in his next 6 throws) = .05 .95
e) None of these is correct.
4
2
Use the following to answer questions 9 & 10: The primary air
exchange system on a proposed spacecraft has four separate
components (call them A, B, C, and D) that all must work properly for
the system to operate well. Assume that the probability of any one
component working is independent of the other components. It has
been shown that the probabilities of each component working are P(A)
= .95, P(B) = .90, P(C) = .99, and P(D) = .90.
9) Find the probability that the entire system works properly.
a) .2382
c) .7618
e) None of these.
b) .6561
d) .8145
10) What is the probability that at least one of the four components
will work properly?
a) .000005
c) .761805
e) None of these.
b) .238195
d) .999995
11) If the probability of a basketball player scoring on any shot is .75,
what is the probability that it will take her more than four shots to first
scores on a shot?
a) .0156
c) .0039
e) None of these.
b) .9961
d) .0118
12) Which of the following is an outcome of a binomial experiment?
a) Getting both spades on the first two draws from a standard deck of
cards, when the first card is not replaced before the second card is
drawn
b) Getting three spades out of the first seven draws from a standard
deck of cards, when each card is not replaced before the next card is
drawn
c) Getting three spades out of the first seven draws from a standard
deck of cards, when each card is replaced before the next card is drawn
d) Getting three spades and four hearts out of the first seven draws
from a standard deck of cards, when each card is not replaced before
the next card is drawn
e) Getting three spades and four hearts out of the first seven draws
from a standard deck of cards, when each card is replaced before the
next card is drawn
For questions 13-16, select the most appropriate probability model for
the given situation. Answers may be used more than once or not at all.
Do not calculate the probabilities.
a) binomial
b) geometric
c) Poisson
d) None of these.
_____ 13) What is the probability that the first base hit will occur
during the fourth at-bat if the probability that the hitter gets a bas hit is
.27 for any at-bat?
_____ 14) What is the probability that a family with 6 children will
have 3 boys and 3 girls?
_____ 15) At a certain intersection, there is an average of two
accidents per week. What is the probability that at least five accidents
will occur in the next two week period?
_____ 16) What is the probability that a shipment of 100 fruit will
have no more than 6 rotten fruits if the probability that any one fruit is
rotten is .04?