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Unformatted text preview: Chapter 17 Probability Models (Review) Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether a probability model based on Bernoulli trials can be used to investigate the situation. If not, explain.
1) You roll a die 4 times and need to get at least three 3's to win the game. 1)
A) Yes
B) No. 3 is more than 10% off;
C) No. More than two outcomes are possible on each roli of the die.
D) No. The rolls are not independent of each other.
E) No. The chance of a getting a 3 changes with each roli of the die. 2) We deal 6 cards from a deck and get 3 spades. How likely is this? 2)
A) Yes.
B) No. 3 is more than 10% of 6
C) No. More than two outcomes are possible on each trial.
D) No. The suit of each card is independent of the suits already obtained. E) No. The chance of getting a spade changes as cards are deait. 3) We draw a card from a deck 10 times to find the distribution of the suits. After each draw the card 3)
is replaced. A) Yes B) N o. More than two outcomes are possible on each trial. C) No. 10 is more than 10% of 52 D) No. The chance of getting each suit changes from one draw to the next. E) No. The draws are not independent of each other. 4) A pool of possible jurors consists of 11 men and 14 women. A jury of 12 is picked at random from 4)
this group. What is the probability that the jury contains all women? A) Yes
B) No. The chance of a woman changes depending on who has already been picked.
C) No. There are more than two possible outcomes on each trial. D) No. 11 is more than 10% of 14 E) Yes, assuming the possibie jurors are unrelated 5) A company realizes that 5% of its pens are defective. In a package of 30 pens, is it likely that more 5)
than 6 are defective? Assume that pens in a package are independent of each other. A) Yes B) No. There are more than two possible outcomes. C) No. The pens in a package are dependent on each other.
D) No. 6 is more than 10% of 30 ' E) No, the chance of getting a defective pen changes depending on the pens that have already
been selected. SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 6) Suppose 16% of students at one college speak Spanish. You Wish to investigate how many 6)
students speak Spanish among 6 students selected at random from the coliege. Describe
how you would use random numbers to simulate the number of Spanish speakers among
the 6 students. 7) Suppose that 70% of applicants for a job have the required quab'ﬁcations. You wish to 7)
investigate the number of applications you might have to check before finding a qualiﬁed
applicant. Describe how you would use random numbers to simuIate the number of
applications you will need to check. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Calculate the probability model. 8) A basketball player makes 60% of her foul shots. You are interested in the number of shots she will 8)
have to attempt until she makes her first shot. Find the probability model. 5 "d H!
V IH
IE
IE
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I w 2 3 4 2 5
P(x) 0.24 0.096 0.0384 0.01536 2 3 4: 2 5
P(x) 0.4 0.24 0.144 0.0864 0.12.96 2 3 4 2 5
P(x) 0.36 0.216 0.1296 0.07776 1 2 3 4 z 5
P(x) 0.24 0.096 0.0384 0.0256 1 4 a 5
P(x) 0.4 0.24 0.144 0.0864 0.05184 m U r) w >
v V v V ‘n—l 9) A basketball player makes 30% of her foul shots. She shoots 5 foul shots. You are interested in the
number of shots that she makes out of the 5. Find the probability model. '
———— 2 3 4 1°(x) 0.16807 0.07203 0.03087 0.01323 0.00567 0.00243 2 3 4 13(x) 0.00243 0.02835 0.1323 0.3087 0.36015 0.16807 2 P(X) 0.00243 0.00567 0.01323 0.03087 0.07203 0.16807 2 3 4
0.36015 0.3087 0.1323 0.02835 0.00243 52 .9 ES 3:
I! II I! II Pa) 0.16807 1 0.00243 E711
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ll P(x) 0. Find the indicated probability. 10) Suppose a computer chip manufacturer rejects 3% of the chips produced because they fail presale
testing. What is the probability that the seventh chip you test is the first bad one you ﬁnd? A) 0.0219 B) 0.03 C) 0.0007 D) 0.21 E) 0.0250 11) An archer is able to hit the bull's eye 71% of the time. If she shoots 10 arrows, what is the probability that her ﬁrst bull's—eye comes on the 4th arrow? Assume each shot is independent of
the others. A) 0.10379 B) 0.02439 C) 0.00502 D) 0.71 E) 0.01732 12) Suppose that 13% of people are left handed. it 8 people are picked at random, What's the
probability that the first lefty is the 8th person chosen? A) 0.1300 13) 0.0490 C) 0.0427 D) 0.3282 E) 0.3773 13) Assume that 25% of people are ieft~handed If we select 10 people at random, find the probability
that the first lefty is the third or fifth person chosen. A) 0.25 B) 0.0111 C) 0.8 D) 0.0166 E) 0.2197 9) 10) 11) 12) 13) Find the indicated probability. Round to four decimai places. 14) Suppose that in a certain population 46% of people have type 0 hiood. A researcher selects people 14)
at random from this population. What is the probability that there is a person with type 0 blood
among the first 6 people checked? A) 0.9752 B) 0.0248 C) 0.0459 D) 0.0095 E) 0.0211 15) Suppose a computer chip manufacturer rejects 6% of the chips produced because they fail presaie 15)
testing. What's the probability you find a bad chip within the first 9 you examine? A) 0.03441 B) 0.4270 C) 0.6096 D) 0.0366 E) 0.5730 16) Suppose that 14% of people in one city speak Spanish. What's the probability that we won't find a 16)
person who speaks Spanish before the 6th person? A) 0.404s B) 0.0566 C) 0.0659 0) 01400 E) 0.4704. Solve. Round to two decimal places if necessary. 17) A basketball player has made 67% of his foul shots during the season. Assuming the shots are 1'7)
independent, find the expected number of shots until he misses.
A) 1.49 B) 0.67 C) 3.03 D) 0.33 E) 33 18) Suppose that 19% of students at one college have high blood pressure. it you keep picking students 18) at random from this college, how many students do you expect to test before finding one with high
blood pressure? A) 0.81 B) 5.26 C) 1.23 D) 19 E) 0.19 19) A laboratory worker finds that 1.4% of his blood samples tested positive for the HIV virus. On 19) average, how many blood samples should he expect to test before finding one which tests positive
for the HIV virus? A) 98.6 B) 0.986 C) 1.01 D) 1.4 E) 71.43 20) At one college, 68% of students have credit cards. A credit card company, iooking for new 20)
customers, sets up a booth at the college. it they pick students at random, how many students
should they expect to talk to before finding one who does not have a credit card? A) 0.32 B) 32 C) 68 D) 1.47 E) 3.13
21) Suppose that 79% of tax returns are free of errors. On average ,how many returns should an IRS 21)
auditor expect to check before finding one with errors?
A) 4.76 B) 1.27 C) 79 D) 0.79 E) 21 Find the indicated probability. 22) An archer is able to hit the buii's—eye 49% of the time. If she shoots 10 arrows, what is the 22)
probability that she gets exactly 4 bull'seyes? Assume each shot is independent of the others. A) 0.0010 B) 0.1267 C) 0.7870 D) 0.2130 E) 0.0576 23) A tennis player makes a successful first serve 53% of the time. if she serves7 times, what is the
probability that she gets alt her first serves in? Assume that each serve is independent of the others. A) 0.0051 B) 00055 C) 0.9883 D) 0.0117 E) 0.0822 24) A multiple choice test has 10 questions each of which hasti possible answers, oniy one of which is
correct. If Judy, who forgot to study for the test, guesses on all questions, what is the probability
that she will answer none of the questions correctly? A) 0.0000010 33) 0.0563 C) 0.0141 D) 0.9999990 E) 0.1074 25) In one city, the probability that a person will pass his or her driving test on the first attempt i50.61.
11 people are selected at random from among those taking their driving test for the first time. What is the probabiiity that among these 11 people, the number passing the test is betWeen 2 and 4
inclusive? A) 0.0827 B) 0.0965 C) 0.0200 D) 0.0870 E) 0.0670 find the probability of the outcome described. 26) A test consists of 10 true/false questions. If a student guesses on each question, what is the
probability that the student wiil answer at ieast9 questions correctly. A) 0.9 B) 0.011 C) 0.999 D) 0.010 E) 0.001 27) A beginning archer is able to hit the bull's—eye 39% of the time. if she shoots6 arrows, what is the
probability that she gets at most 3 bull’sweyes? Assume each shot is independent of the others. A) 0.2693 B) 0.5650 C) 01657 D) 0.1190 E) 0.8343 28) A tennis player makes a successfui ﬁrst serve 55% of the time. if she serves 10 times, what is the
probability that she gets at least 3 first serves in? Assume that each serve is independent of the
others. A) 0.0274 B) 0.0746 C) 0.9726 D) 0.8980 E) 0.1020 29) A company purchases shipments of machine components and uses this acceptance sampling plan:
Randomly select and test 28 components and accept the whole batch if there are fewer than 3 _ I
defectives. If a particular shipment of thousands of components actualiy has a7% rate of defects,
what is the probability that this whoie shipment wili be accepted? A) 0.6880 B) 0.1831 C) 0.3120 D) 0.5569 ii) 0.2807 30) in a study, 40% of adults questioned reported that their health was exceilent. A researcher wishes to
study the health of people living close to a nuclear power plant. Among 12 adults randomly
selected from this area, only 3 reported that their health was excellent. Find the probability that
when 12 adults are randomly selected, 3 or fewer are in excellent heaith. A) 0.1419 is) 0.7747 C) 0.0834 D) 0.1522 a) 0.2253 23) 24.) 25) 26) 27) 28) 29) 30) 31) A basketball player has made 70% of his foul shots during the season. If he shootsS foul shots in tonight's game, what is the probability that he misses at least once? Assume that shots are
independent of each other. A) 0.8319 B) 0.1681 C) 0.3 D) 0.15 ‘8.) 0.0024 Find the indicated probabiiity. 32) Suppose a computer chip manufacturer rejects 3% of the chips produced because they fail presaie
testing. If you testS chips, What is the probability that none of the clu‘ps fail? A) 0.15 13) 0.8587 C) 0.97 D) 2.43 x 10—8
s) 0.03 33) A basketball player has made 70% of his foul shots during the season. If he shoots é foul shots in
tonight’s game, what is the probability that he makes all of the shots? A) 0.0081 B) 0.12 C) 0.28 D) 0.7 5) 0.2401 34) i’olice estimate that 25% of drivers drive Without their seat belts. If they stop 4 drivers at random,
find the probability that all of them are wearing their seat belts. A) 0.3164. s) 0.1 C) 0.3 D) 0.75 E) 00039 35) A tennis player makes a successful first serve 65% of the time. Assume that each serve is
independent of the others. If she serves 3 times, what is the probability that she makes all of her
first serves? A) 0.65 B) 0.195 C) 0.04.29 D) 0.2746 E) 0.105 36) Suppose a computer chip manufacturer rejects 15% of the chips produced because they fail. presale
testing. If you test4 chips, what is the probability that not all of the chips fall? A) 0.5220 B) 5.06 x 10—4
C) 0.9995 D) 0.6 E) 0.15 37) A tennis player makes a successful ﬁrst serve 65% of the time. Assume that each serve is independent of the others. If she serves?) times, what is the probability that she does not make all of
her first serves? A) 0.65 8) 0.7254 C) 0.0429 D) 0.2746 H) 0.105 31) 32) 33) 34.) 35) 36) 37) Soive the problem. 38) Suppose a computer chip manufacturer rejects 5% of the chips produced because they fail presale 38)
testing. If we select 50 chips at random, how many chips do you expect to fail the testing? A) 2.5 chips B) 0.05 chips C) 5 chips D) 2 chips E) 21.8 chips 39) An archer is able to hit the buii's eye 56% of the time. if she shoots’? arrows, how many buii’s—eyes 39)
do you expect her to get? Assume the shots are independent of each other. A) 3.5 B) 3.92 C) 3.08 D) 1.724s E) 1.3 40) Police estimate that in one city 59% of drivers wear their seat belts. They Set up a safety roadblock, 40)
stopping cars to check for seat belt use. If they stop 30 cars during the first hour, what is the mean
of the number of drivers expected to be wearing their Seat belts? A) 7.26 B) 17.7 C) 15 D) 12.3 E) 2.69
41) A laboratory worker finds that 2.3% of his biood samples test positive for the HIV virus. In a 41)
random sample of 70 blood tests, what is the mean number that test positive for the HIV virus?
A) 68.39 B) 1.57 C) 1.25 D) 1.61 E) 16.1
42) Suppose the probabiiity of a major earthquake on a given day is 1 out of 10,000. What's the 42)
expected number of earthquakes in the next 2000 days?
1 1 1
A) 10,000 B) 20 C) 5 D) 2000 E) “5" 43) On a multiple choice test with 13 questions, each question has four possible answers, one of which 43)
is correct. For students who guess at all answers, find the standard deviation of the number of correct answers.
A) 1.561 B) 1.47 C) 1.875 D) 1.5 E) 1.58
44) A company manufactures batteries in batches of 30 and there is a 3% rate of defects. Find the 4.4)
standard deviation of the number of defects per batch.
A) 0.949 B) 0.934 C) 0.919 D) 0.931 E) 0.291
45) A tennis player makes a successful first serve 66% of the time. If she serves 43 times, what is the 45)
standard deviation of the number of good ﬁrst serves? Assume that each serve is independent of
the others.
A) 28.38 B) 21.5 C) 9.6492 D) 3.11, E) 14.62
46) Suppose that 1.8% of peopie are left handed. If 40 people are selected at random, What is the 46)
standard deviation of the number of right—handers in the group?
A) 070704 B) 0.84 C) 0.72 D) 6.27 E) 0.85 47) In the town of Blue Valley, 5% of female college students suffer from manic—depressive iliness. If 47)
130 of the female students are selected at random, what is the standard deviation of the number
who suffer from manicmdepressive illness? A) 6.5 B) 2.55 C) 2.48 D) 6.18 E) 123.5 Describe an appropriate normal model that can be used to approximate the binomial distribution. If it is not appropriate
to use a normal approximation, give a reason Why not. 48) An archer is able to hit the bull's eye 78% of the time. If she shoots 120 arrows in a competition, is it 48)
appropriate to use a normal model to approximate the distribution of the number of bull's—eyes?
Assume that shots are independent of each other. A) Yes; normal model with u = 93.6 and o m 4.54 can be used to approximate the distribution
B) Yes; normal model with u = 26.4 and o m 20.59 can be used to approximate the distribution
C) No; normal model cannot be used to approximate the distribution because np< 10 D) No; normal model cannot be used to approximate the distribution because nq< 10 E) Yes; normal model with u = 93.6 and o = 20.59 can be used to approximate the distribution 49) Suppose a computer chip manufacturer rejects 3% of the chips produced because they fail presale 49)
testing. If 100 chips are picked at random, is it appropriate to use a normal model to approximate
the distribution of the number of bad chips? A) Yes; normal model with u m 97 and o z 1.71 can be used to approximate the distribution
B) Yes; normal model with u m 3 and o x 1.71 can be used to approximate the distribution
C) No; normal model cannot be used to approximate the distribution because up < 10 D) Yes; normal model with u n 3 and o z 2.91 can be used to approximate the distribution 13) No; normal model cannot be used to approximate the distribution because nq < 10 50) In one city, police estimate that 90% of drivers wear their seat belts. They set up a safety roadblock 50)
and they stop drivers to check for seat belt use. 3200 drivers are stopped, is it appropriate to use a
normal model to approximate the distribution of the number whose seat belt is not buckled? A) Yes; normal model with p. u 20 and or m 18.00 can be used to approximate the distribution
B) Yes; normal model with u w 20 and 0 w 4.24 can be used to approximate the distribution
C) No; normal model cannot be used to approximate the distribution because np < 10 D) Yes; normal model with u m 180 and o m 4.24: can be used to approximate the distribution E) No; normai model cannotbe used to approximate the distribution because nq < 10 Find the indicated probability by using an appropriate normal model to approximate the binomial distributio: 51) An archer is able to hit the bull's eye 76% of the time. If she shoots 160 arrows in a competition, 51)
What's the probability that she gets at least 130 bull’sweyes? Assume that shots are independent of
each other. A) 0.060 B) 0.067 C) 0.386 D) 0614 E) 0.939 52) Bill claims that he has a coin which is biased and which comes up heads more than tails. His claim 52)
is based on a trial in which he ﬂipped the coin 200 times and got 110 heads. If the coin were actually
fair, what would be the probability of getting 110 or more heads? A) 09213 B) 0.0787 C) 0.42.11 D) 0.5789 F.) 0.0591 53) An airline, believing that 6% of passengers fail to show up for flights, overbooks. Suppose a plane 53)
will hold 320 passengers and the airline sells 335 seats. What’s the probability the airline will not
have enough seats and will have to bump someone? A) 0.0751 B) 0.9197 C) 0.3745 33) 0.0803 E) 0.1204 54) In the town of Blues Vaiiey, 5% of college students suffer from manicdepressive illness. if 300 of 54)
the students are selected at random and screened, what is the probability that no more than 20 of
them suffer from manic—depressive illness? A) 0.8485 13) 0.9074 C) 0.3632 D) 0.6368 E) 0.0926 55) An airline has found that on average, 8% of its passengers request vegetarian meals. On a flight 55) with 360 passengers the airline has 35 vegetarian dinners available. What's the probability that it
will be short of vegetarian dinners? A) 0.9190 B) 0.6059 C) 0.3941 D) 0.0810 E) 0.0668 i’rovide an appropriate response. 56) A basketbaii player usually makes 57% of his free shots. Tonight he made 9 shots in a row. Is this 56)
evidence that he is on a winning streak? That is, is this streak so unusual that it means the
probability he makes a shot must have changed? Explain. A) Yes; if his success rate were sti1157%, he would have only a 0.6% chance of making 9 shots in a
row. That's an unusual result. B) No; if his success rate were still 57%, he would have a 5.1% chance of making 9 shots in a row.
That's not a highly unusual result. C) Yes; if his success rate were still 57%, he would have only a 5.1% chance of making 9 shots in a
row. That's an unusual result. D) No; if his success rate were still 57%, he would have a 0.6% chance of making 9 shots in a row.
That‘s not an unusual result. E) Yes; if his success rate were 30115796, he would have only a 0.4% chance of making 9 shots in a
now. That's an unusual result. 10 5'7) A tennis player usually makes a successful first serve 73% of the time. She buys a new racket 57)
hoping that it will improve her success rate. During the first month of playing with her new racket
she makes 327 successful first serves out of 410. Is this evidence that with the new racket her
success rate has improved? in other words, is this an unusual result for her? Explain. A) Yes; we would normally expect her to make 299.3 first serves with a standard deviation of
8.99. 327 is 3.1 standard deviations above the expected value. That's an unusual result. l3) Yes; we would normally expect her to make 299.3 first serves with a standard deviation of
80.81. 327 is 0.3 standard deviations above the expected value. That’s an unusual result. C) No; we would normally expect her to make 299.3 first serves with a standard deviation of
80.81. 327 is 0.3 standard deviations above the expected value. That’s not an unusual result. D) No; we would normally expect her to make 299.3 first serves with a standard deviation of
8.99. 327 is 3.1 standard deviations above the expected value. That's not an unusual result. E) No; we would no...
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 Spring '09
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