Download Chapter 8 Practice Test – Binomial and

AP Statistics
Chapter 8 Practice Test
Name:_________________________
Date:__________Period:_________
Chapter 8 Practice Test – Binomial and Geometric Distributions
Part 1: Multiple Choice. Hand write the letter corresponding to the best answer in space provided on page 3.
_____1. Sixty-five percent of all divorce cases cite incompatibility as the underlying reason. If four
couples file for a divorce, what is the probability that exactly two will state incompatibility as the
reason?
a) .104
b) .207
c) .254
d) .311
e) .423
_____2. Which of the following are true statements?
I.
II.
III.
a)
b)
c)
d)
e)
The histogram of a binomial distribution with p = .5 is always symmetric.
The histogram of a binomial distribution with p = .9 is skewed to the right.
The histogram of a geometric distribution with is always decreasing.
I and II
I and III
II and III
I, II, and III
None of the above gives the complete set of complete responses.
_____3. Binomial and geometric probability situations share many conditions. Identify the choice that
is not shared.
a) The probability of success on each trial is the same.
b) There are only two outcomes on each trial.
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) The mean depends on the probability of a success.
_____4. An inspection procedure at a manufacturing plant involves picking thirty items at random and
then accepting the whole lot if at least twenty-five of the thirty items are in perfect condition. If in
reality 85% of the whole lot is perfect, what is the probability that the lot will be accepted?
a) .524
b) .667
c) .186
d) .476
e) .711
_____5. A recent study of the Livingston High School student body determined that 41% of the
students were “chic”. If Mrs. Poyner has developed a test for “chic-ness”, what is the average
number of students we would need to test in order to find one who is “chic”?
a) 2
b) 2.43
c) 3
d) 3.57
e) 1, because the study is clearly in error since all LHS students are “chic”
Mrs. Poyner/ Mr. Page
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AP Statistics
Chapter 8 Practice Test
_____6. Circuit boards are assembled by selecting 4 computer chips at random from a large batch of
chips. In this batch of chips, 90 percent of the chips are acceptable. Let X denote the number of
acceptable chips out of a sample of 4 chips from this batch. What is the least probable value of X?
a) 0
b) 1
c) 2
d) 3
e) 4
_____7. The color distribution in a bag of Reese’s Pieces was found to be 13 brown, 22 orange, and 15
yellow. If a piece is randomly drawn and replaced, what is the probability that it will take less than 8
draws to get an orange piece?
a) .014
b) .008
c) .990
d) .983
e) .500
_____8. A probability experiment involves a series of identical, independent trials with two outcomes
(success/failure) per trial and the probability of a success on each trial is 0.1. Determine the number of
trials, n, in a binomial experiment such that the expected number of successes in that binomial
experiment will be equal to the expected number of trials in a geometric experiment.
a) 2
b) 5
c) 10
d) 50
e) 100
_____9. Which of the following statements is NOT correct?
a) The number of successes that corresponds to the maximum value of a binomial PDF is within
one unit of it’s mean.
b) A geometric PDF is always decreasing.
c) A binomial PDF with p < .5 will be skewed right.
d) As the number of trials in a geometric situation increases and the number of successes in a
binomial situation increases, the value of the CDF approaches 0.
e) A PDF can be transformed into a CDF by using addition.
_____10. A professional basketball player sinks 80% of his foul shots, in the long run. If he gets 100
tries during a season, then the probability that he sinks between 75 and 90 shots (inclusive) is
a) P(-1.25  z  2.5)
b) P(-1.125  z  2.625)
c) P(-1.125  z  2.375)
d) P(-1.375  z  2.375)
e) P(-1.375  z  2.625)
Mrs. Poyner/ Mr. Page
page 2
AP Statistics
Chapter 8 Practice Test
Name:___________________________
Date:_____________Period:________
PART I answers
1.
2.
3.
4.
5.
6.
7.
8.
9
10.
PART II - Answer completely, but be concise. Write sequentially and show all steps. Show all your
work. Indicate clearly the methods you used, because you will be graded on the correctness of your
methods as well as on the accuracy of your results and explanations.
YOU MUST WRITE ANSWERS IN BY HAND – you need not print out the first 3 pages.
11. Statistics on Teens and Television: Percentage of teenagers 13-17 who can name the city where
the US Constitution was written (Philadelphia): 25. Percentage of teenagers 13-17 who know where
you find the zip code 90210 (Beverly Hills): 75 (Survey conducted by the National Constitution
Center (NCC), Philadelphia, 1998.)
a) Find the probability that the fourth teenager that is asked to name the city where the US
Constitution was written is the first to know it was Philadelphia. Then find the same for the
Beverly Hills question. (Assume each observation is independent).
b) Find the probability that it takes more than 4 teenagers to observe the first teen that answers
correctly when asked to name the city where the US Constitution was written. Then find the same
for the Beverly Hills question. (Assume each observation is independent).
c) Find the mean and variance of the number of teenagers that would have to be asked in order to
find the first person that could correctly respond when asked to name the city where the US
Constitution was written. Then do the same for the Beverly Hills question.
Mrs. Poyner/ Mr. Page
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AP Statistics
Chapter 8 Practice Test
d) In comparing the two different distributions, briefly try to explain why you think there is a
difference between the two.
12. One theory of flocking is that birds flock to increase efficiency in looking for any approaching
predators (“scanning.”) Because birds can barely move their eyes they must turn their heads to look
for predators, making them temporarily unable to peck for food. If the birds flock together, each
could spend less time scanning; when any bird detects a predator it squawks and flies away, alerting
the other birds.
The Chanting Goshawk, Melierax metabetes, is a predator of the Red-billed Weaver bird, Quelea
quelea. From field experiments it is known that the individual weaver bird has a probability of
approximately 0.20 of detecting a goshawk in time to fly away. Suppose that the flocking theory is
false; that is, even when flocking each bird scans for predators independently. Suppose further that a
goshawk suddenly comes upon a flock of 4 weaver birds pecking for food on the ground, and goes
into predator mode.
a) What is the probability that none of the weaver birds will detect the goshawk’s presence before
it is too late, thus allowing the goshawk to have a weaver bird lunch?
b) What is the probability that at least one of the weaver birds will detect the goshawk’s presence,
thus alerting the others and all fly away, leaving the goshawk hungry?
c) Suppose this is Wednesday, and all the weaver birds flock in groups of 4 on Wednesdays.
Using your results from (a) and/or (b), find the probability that a random goshawk, flying randomly,
will go hungry until swooping down on the 5th flock of weaver birds seen that day.
Mrs. Poyner/ Mr. Page
page 4
AP Statistics
Chapter 8 Practice Test
13. Men’s pant sizes are determined by their measure around the waist. Suppose that men’s waist sizes
are approximately normally distributed with a mean of 35.8 inches and standard deviation 2.2
inches. A retailer sells men’s pants in sizes XS, S, M, L, XL, where the pant sizes are defined in the
table below.
Pant size
XS
S
M
L
XL
Waist size
31  waist size< 33
33  waist size< 35
35  waist size< 37
37  waist size< 39
39  waist size< 41
a) Because the retailer only stocks the sizes listed above, what proportion of customers will find the
retailer does not carry any pairs of pants in their size? Show your work.
b) Using a sketch of a normal curve, illustrate the proportion of men whose pant size is L.
Calculate this proportion.
c) Of 15 randomly selected customers, what is the probability that exactly 5 will request size L.
Show your work.
Mrs. Poyner/ Mr. Page
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