Download Ch. 4, 5, 6 - Math Department

Ch. 4, 5, 6
Name___________________________________
03/24/2010
Math 227 Exam #2
_____________________________________________________________________________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Make
sure that you input all you answers on the correct ScanTron.
Express the indicated degree of likelihood as a probability value.
1) "You have a 50-50 chance of choosing the correct answer."
A) 50
B) 0.9
C) 0.25
2) "There is a 40% chance of rain tomorrow."
A) 40
B) 4
C) 0.40
D) 0.50
D) 0.60
3) "You cannot determine the exact decimal-number value of ."
A) 1
B) 0.5
C) 0
D) 3.14
4) "It will definitely turn dark tonight."
A) 0.67
B) 1
C) 0.30
D) 0.5
5) "You have one chance in ten of winning the race."
A) 0.5
B) 0.10
C) 1
D) 0.90
5
C)
3
1
D)
2
Answer the question.
6) Which of the following cannot be a probability?
2
3
A)
B)
3
5
7) What is the probability of an impossible event?
A) -1
B) 0.1
C) 1
D) 0
8) On a multiple choice test with four possible answers for each question, what is the probability of
answering a question correctly if you make a random guess?
1
1
3
A)
B)
C)
D) 1
2
4
4
Find the indicated probability.
9) A sample space consists of 14 separate events that are equally likely. What is the probability of
each?
1
A) 1
B) 0
C)
D) 14
14
1)
2)
3)
4)
5)
6)
7)
8)
9)
10) On a multiple choice test, each question has 7 possible answers. If you make a random guess on
the first question, what is the probability that you are correct?
1
A) 7
B)
C) 0
D) 1
7
10)
11) A die with 8 sides is rolled. What is the probability of rolling a number less than 7?
1
7
3
A)
B)
C) 6
D)
8
8
4
11)
1
12) A bag contains 2 red marbles, 3 blue marbles, and 5 green marbles. If a marble is randomly
selected from the bag, what is the probability that it is blue?
1
3
1
1
A)
B)
C)
D)
5
10
3
7
12)
13) Two 6-sided dice are rolled. What is the probability that the sum of the two numbers on the dice
will be 4?
2
11
1
A) 3
B)
C)
D)
3
12
12
13)
14) If a person is randomly selected, find the probability that his or her birthday is in May. Ignore leap
years.
31
1
1
1
A)
B)
C)
D)
365
12
365
31
14)
15) In a poll, respondents were asked whether they had ever been in a car accident. 127 respondents
indicated that they had been in a car accident and 299 respondents said that they had not been in a
car accident. If one of these respondents is randomly selected, what is the probability of getting
someone who has been in a car accident? Round to the nearest thousandth, if necessary.
A) 0.425
B) 0.702
C) 0.008
D) 0.298
15)
Answer the question, considering an event to be "unusual" if its probability is less than or equal to 0.05.
16) Is it "unusual" to get a 12 when a pair of dice is rolled?
A) No
B) Yes
17) Is it "unusual" to get 6 when a pair of dice is rolled?
A) No
B) Yes
16)
17)
18) Assume that a study of 300 randomly selected school bus routes showed that 280 arrived on time.
Is it "unusual" for a school bus to arrive late?
A) Yes
B) No
18)
19) Assume that a study of 500 randomly selected school bus routes showed that 478 arrived on time.
Is it "unusual" for a school bus to arrive late?
A) Yes
B) No
19)
20) If you are told that a mystery person's name begins with a consonant, would it be "unusual" to
guess the first letter of that person's name?
A) No
B) Yes
20)
21) If you drew one card from a standard deck, would it be "unusual" to draw a 5?
A) Yes
B) No
21)
22) Assume that one student in your class of 27 students is randomly selected to win a prize. Would it
be "unusual" for you to win?
A) No
B) Yes
22)
2
Estimate the probability of the event.
23) The data set represents the income levels of the members of a country club. Estimate the
probability that a randomly selected member earns at least $79,000. Round your answers to the
nearest tenth.
23)
89,000 99,000 69,000 104,000 74,000 89,000 79,000 59,000 114,000 139,000 64,000 84,000 109,000
74,000 99,000 94,000 79,000 119,000 54,000 94,000
A) 0.4
B) 0.7
C) 0.8
D) 0.6
24) Of 1085 people who came into a blood bank to give blood, 340 people had high blood pressure.
Estimate the probability that the next person who comes in to give blood will have high blood
pressure.
A) 0.313
B) 0.232
C) 0.281
D) 0.364
24)
25) In a certain class of students, there are 10 boys from Wilmette, 5 girls from Winnetka, 8 girls from
Wilmette, 5 boys from Glencoe, 3 boys from Winnetka and 8 girls from Glenoce. If the teacher
calls upon a student to answer a question, what is the probability that the student will be a boy?
A) 0.742
B) 0.256
C) 0.462
D) 0.385
25)
From the information provided, create the sample space of possible outcomes.
26) Flip a coin three times.
A) HHH HHT HTH HTT THH THT TTH TTT
B) HTT THT HTH HHH TTH TTT
C) HHH TTT THT HTH HHT TTH HTH
D) HHH HTT HTH TTT HTT THH HHT THT
27) Both Fred and Ed have a bag of candy containing a lemon drop, a cherry drop, and a lollipop. Each
takes out a piece and eats it. What are the possible pairs of candies eaten?
A) LD-LD CD-LD LP-LP LD-LP CD-CD LD-LP LP-CD CD-LD LP-LD
B) CD-LD LD-LP LP-CD LP-LP LD-LD
C) LD-LD CD-LD LP-LP LD-CD CD-CD LD-LP LP-CD CD-LP LP-LD
D) LD-CD LD-CD LD-CD LD-LP LD-LP LD-LP CD-LP CD-LP CD-LP
Answer the question.
28) In a certain town, 25% of people commute to work by bicycle. If a person is selected randomly
from the town, what are the odds against selecting someone who commutes by bicycle?
A) 1 : 3
B) 3 : 1
C) 3 : 4
D) 1 : 4
29) Suppose you are playing a game of chance. If you bet $7 on a certain event, you will collect $259
(including your $7 bet) if you win. Find the odds used for determining the payoff.
A) 1 : 36
B) 37 : 1
C) 36 : 1
D) 259 : 266
Determine whether the events are mutally exclusive.
30) Meet a man with an umbrella.
Meet a man with a raincoat.
A) No
26)
27)
28)
29)
30)
B) Yes
31) Get a full time day job as a teller with a bank.
Get a full time day job as a cashier at a store.
A) Yes
31)
B) No
3
32) Go to a formal dinner affair.
Wear blue jeans.
A) No
32)
B) Yes
33) Get stung by a bee.
Get stung by a wasp.
A) Yes
33)
B) No
Find the indicated probability.
34) Find P(A), given that P(A) = 0.839.
A) 0
B) 1.839
C) 1.192
D) 0.161
34)
35) Based on meteorological records, the probability that it will snow in a certain town on January 1st
is 0.455. Find the probability that in a given year it will not snow on January 1st in that town.
A) 0.545
B) 2.198
C) 1.455
D) 0.835
35)
36) The probability that Luis will pass his statistics test is 0.74. Find the probability that he will fail his
statistics test.
A) 0.26
B) 2.85
C) 1.35
D) 0.37
36)
37) If a person is randomly selected, find the probability that his or her birthday is not in May. Ignore
leap years.
11
334
31
31
A)
B)
C)
D)
12
365
334
365
37)
38) A spinner has equal regions numbered 1 through 21. What is the probability that the spinner will
stop on an even number or a multiple of 3?
2
10
1
A)
B)
C) 17
D)
3
9
3
38)
39) If you pick a card at random from a well shuffled deck, what is the probability that you get a face
card or a spade?
1
11
25
9
A)
B)
C)
D)
22
26
52
26
39)
40) The table below describes the smoking habits of a group of asthma sufferers.
Occasional Regular
Heavy
Nonsmoker
smoker smoker smoker Total
Men
340
34
74
37
485
Women
398
39
74
50
561
Total
738
73
148
87
1046
40)
If one of the 1046 people is randomly selected, find the probability that the person is a man or a
heavy smoker.
A) 0.511
B) 0.476
C) 0.547
D) 0.425
4
41) Of the 68 people who answered "yes" to a question, 12 were male. Of the 87 people that answered
"no" to the question, 8 were male. If one person is selected at random from the group, what is the
probability that the person answered "yes" or was male?
A) 0.129
B) 0.176
C) 0.49
D) 0.568
41)
42) A study of consumer smoking habits includes 163 people in the 18-22 age bracket (44 of whom
smoke), 140 people in the 23-30 age bracket (37 of whom smoke), and 81 people in the 31-40 age
bracket (25 of whom smoke). If one person is randomly selected from this sample, find the
probability of getting someone who is age 23-30 or smokes.
A) 0.641
B) 0.264
C) 0.096
D) 0.544
42)
43) A study of consumer smoking habits includes 177 people in the 18-22 age bracket (43 of whom
smoke), 134 people in the 23-30 age bracket (30 of whom smoke), and 86 people in the 31-40 age
bracket (29 of whom smoke). If one person is randomly selected from this sample, find the
probability of getting someone who is age 18-22 or does not smoke.
A) 0.757
B) 1.189
C) 0.338
D) 0.851
43)
44) 100 employees of a company are asked how they get to work and whether they work full time or
part time. The figure below shows the results. If one of the 100 employees is randomly selected,
find the probability of getting someone who carpools or someone who works full time.
44)
1. Public transportation: 9 full time, 7 part time
2. Bicycle: 3 full time, 4 part time
3. Drive alone: 31 full time, 28 part time
4. Carpool: 9 full time, 9 part time
A) 0.61
B) 0.54
C) 0.28
D) 0.14
45) A card is drawn from a well-shuffled deck of 52 cards. Find P(drawing an ace or a 9).
13
2
4
A)
B) 8
C)
D)
2
13
13
45)
46) A card is drawn from a well-shuffled deck of 52 cards. Find P(drawing a face card or a 4).
2
12
4
A) 16
B)
C)
D)
13
13
13
46)
5
47) The table below describes the smoking habits of a group of asthma sufferers.
Occasional Regular Heavy
Nonsmoker
smoker
smoker smoker Total
Men
328
36
80
31
475
Women
340
37
60
45
482
Total
668
73
140
76
957
47)
If one of the 957 people is randomly selected, find the probability of getting a regular or heavy
smoker.
A) 0.146
B) 0.116
C) 0.514
D) 0.226
48) A bag contains 7 red marbles, 4 blue marbles, and 1 green marble. Find P(not blue).
1
2
3
A)
B) 8
C)
D)
3
3
2
48)
49) The probability that an event will occur is 0.3. What is the probability that the event will not occur?
49)
A) 0
C)
B) 0.7
3
7
D) None of the above is correct.
50) In one town, 31% of all voters are Democrats. If two voters are randomly selected for a survey,
find the probability that they are both Democrats.
A) 0.620
B) 0.096
C) 0.310
D) 0.093
50)
51) Find the probability of correctly answering the first 2 questions on a multiple choice test if random
guesses are made and each question has 3 possible answers.
1
1
3
2
A)
B)
C)
D)
8
9
2
3
51)
52) A manufacturing process has a 70% yield, meaning that 70% of the products are acceptable and
30% are defective. If three of the products are randomly selected, find the probability that all of
them are acceptable.
A) 0.429
B) 0.027
C) 2.1
D) 0.343
52)
53) A batch consists of 12 defective coils and 88 good ones. Find the probability of getting two good
coils when two coils are randomly selected if the first selection is replaced before the second is
made.
A) 0.176
B) 0.7744
C) 0.7733
D) 0.0144
53)
54) A bin contains 77 light bulbs of which 10 are defective. If 5 light bulbs are randomly selected from
the bin with replacement, find the probability that all the bulbs selected are good ones.
A) 0.499
B) 0.543
C) 0
D) 0.87
54)
55) In one town, 64% of adults have health insurance. What is the probability that 6 adults selected at
random from the town all have health insurance?
A) 0.069
B) 0.64
C) 0.094
D) 3.84
55)
6
56) A study conducted at a certain college shows that 52% of the school's graduates find a job in their
chosen field within a year after graduation. Find the probability that 9 randomly selected
graduates all find jobs in their chosen field within a year of graduating.
A) 0.173
B) 4.680
C) 0.005
D) 0.003
56)
57) Find the probability that 2 randomly selected people all have the same birthday. Ignore leap years.
A) 0.0055
B) 0.00273973
C) 0.5
D) 0.00000751
57)
Provide a written description of the complement of the given event.
58) When 10 adults are tested for high blood pressure, at least one of the results are positive.
A) All of the adults have high blood pressure.
B) Nine of the adults have high blood pressure.
C) None of the adults have high blood pressure.
59) When 100 engines are shipped, all of them are free of defects.
A) At least one of the engines is defective.
B) None of the engines are defective.
C) All of the engines are defective.
Find the indicated probability.
60) An unprepared student makes random guesses for the ten true-false questions on a quiz. Find the
probability that there is at least one correct answer.
1
1
9
1,023
A)
B)
C)
D)
10
1,024
10
1,024
58)
59)
60)
61) A study conducted at a certain college shows that 57% of the school's graduates find a job in their
chosen field within a year after graduation. Find the probability that among 8 randomly selected
graduates, at least one finds a job in his or her chosen field within a year of graduating.
A) 0.125
B) 0.570
C) 0.989
D) 0.999
61)
62) A sample of 4 different calculators is randomly selected from a group containing 11 that are
defective and 30 that have no defects. What is the probability that at least one of the calculators is
defective?
A) 0.713
B) 0.729
C) 0.110
D) 0.271
62)
63) In a batch of 8,000 clock radios 7% are defective. A sample of 6 clock radios is randomly selected
without replacement from the 8,000 and tested. The entire batch will be rejected if at least one of
those tested is defective. What is the probability that the entire batch will be rejected?
A) 0.0700
B) 0.353
C) 0.167
D) 0.647
63)
64) In a blood testing procedure, blood samples from 6 people are combined into one mixture. The
mixture will only test negative if all the individual samples are negative. If the probability that an
individual sample tests positive is 0.12, what is the probability that the mixture will test positive?
A) 0.536
B) 0.00000299
C) 1.00
D) 0.0144
64)
7
65) The table below shows the soft drinks preferences of people in three age groups.
cola root beer lemon-lime
under 21 years of age 40
25
20
between 21 and 40 35
20
30
over 40 years of age 20
30
35
65)
If one of the 255 subjects is randomly selected, find the probability that the person is over 40 years of
age.
1
1
3
2
A)
B)
C)
D)
3
2
5
5
66) The table below shows the soft drinks preferences of people in three age groups.
cola root beer lemon-lime
under 21 years of age 40
25
20
between 21 and 40 35
20
30
over 40 years of age 20
30
35
66)
If one of the 255 subjects is randomly selected, find the probability that the person is over 40 and
drinks cola.
4
4
A)
B)
17
51
C)
4
19
D) None of the above is correct.
67) The table below shows the soft drinks preferences of people in three age groups.
cola root beer lemon-lime
under 21 years of age 40
25
20
between 21 and 40 35
20
30
over 40 years of age 20
30
35
67)
If one of the 255 subjects is randomly selected, find the probability that the person is over 40 years of
age given that they drink root beer.
5
2
A)
B)
17
5
C)
6
17
D) None of the above is correct.
68) The table below shows the soft drinks preferences of people in three age groups.
cola root beer lemon-lime
under 21 years of age 40
25
20
between 21 and 40 35
20
30
over 40 years of age 20
30
35
If one of the 255 subjects is randomly selected, find the probability that the person drinks root beer
given that they are over 40.
2
6
A)
B)
5
17
C)
2
17
D) None of the above is correct.
8
68)
69) The following table contains data from a study of two airlines which fly to Small Town, USA.
69)
Number of flights Number of flights
which were on time
which were late
Podunk Airlines
33
6
Upstate Airlines
43
5
If one of the 87 flights is randomly selected, find the probability that the flight selected arrived on
time given that it was an Upstate Airlines flight.
11
43
A)
B)
76
87
C)
43
48
D) None of the above is correct.
70) The following table contains data from a study of two airlines which fly to Small Town, USA.
70)
Number of flights Number of flights
which were on time
which were late
Podunk Airlines
33
6
Upstate Airlines
43
5
If one of the 87 flights is randomly selected, find the probability that the flight selected is an Upstate
Airlines flight given that it was late.
5
5
A)
B)
48
87
C)
5
11
D) None of the above is correct.
71) The following table contains data from a study of two airlines which fly to Small Town, USA.
Number of flights Number of flights
which were on time
which were late
Podunk Airlines
33
6
Upstate Airlines
43
5
If one of the 87 flights is randomly selected, find the probability that the flight selected is an Upstate
Airlines flight which was on time.
43
11
A)
B)
87
76
C)
43
76
D) None of the above is correct.
9
71)
72) The table below describes the smoking habits of a group of asthma sufferers.
Light Heavy
Nonsmoker smoker smoker Total
Men
362
89
60
511
Women
392
61
72
525
Total
754
150
132 1036
72)
If one of the 1036 subjects is randomly selected, find the probability that the person chosen is a
nonsmoker given that it is a woman. Round to the nearest thousandth.
A) 0.520
B) 0.747
C) 0.378
D) 0.407
73) The table below describes the smoking habits of a group of asthma sufferers.
Light Heavy
Nonsmoker smoker smoker Total
Men
380
83
87
550
Women
322
73
67
462
Total
702
156
154 1012
73)
If one of the 1012 subjects is randomly selected, find the probability that the person chosen is a
woman given that the person is a light smoker.
A) 0.468
B) 0.158
C) 0.072
D) 0.254
Solve the problem.
74) There are 11 members on a board of directors. If they must form a subcommittee of 3 members,
how many different subcommittees are possible?
A) 165
B) 1331
C) 6
D) 990
74)
75) The library is to be given 7 books as a gift. The books will be selected from a list of 19 titles. If each
book selected must have a different title, how many possible selections are there?
A) 2.413593262e+13
B) 50,388
C) 1.216451004e+17
D) 253,955,520
75)
76) How many ways can an IRS auditor select 4 of 10 tax returns for an audit?
A) 210
B) 10,000
C) 24
76)
D) 5040
77) A state lottery involves the random selection of six different numbers between 1 and 21. If you
select one six number combination, what is the probability that it will be the winning combination?
1
1
1
1
A)
B)
C)
D)
720
39,070,080
85,766,121
54,264
77)
78) 8 basketball players are to be selected to play in a special game. The players will be selected from a
list of 27 players. If the players are selected randomly, what is the probability that the 8 tallest
players will be selected?
8
1
1
1
A)
B)
C)
D)
27
2,220,075
40,320
213,127,200
78)
10
79) The organizer of a television show must select 5 people to participate in the show. The participants
will be selected from a list of 28 people who have written in to the show. If the participants are
selected randomly, what is the probability that the 5 youngest people will be selected?
2
1
1
1
A)
B)
C)
D)
7
11,793,600
120
98,280
79)
80) How many 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7 if repetition of digits is
not allowed?
A) 5
B) 6
C) 210
D) 343
80)
81) A musician plans to perform 5 selections. In how many ways can she arrange the musical
selections?
A) 5
B) 25
C) 120
D) 720
81)
82) A pollster wants to minimize the effect the order of the questions has on a person's response to a
survey. How many different surveys are required to cover all possible arrangements if there are 6
questions on the survey?
A) 6
B) 720
C) 120
D) 36
82)
83) There are 7 members on a board of directors. If they must elect a chairperson, a secretary, and a
treasurer, how many different slates of candidates are possible?
A) 343
B) 35
C) 210
D) 5040
83)
84) A tourist in France wants to visit 12 different cities. How many different routes are possible?
A) 144
B) 12
C) 479,001,600
D) 39,916,800
84)
85) A tourist in France wants to visit 11 different cities. If the route is randomly selected, what is the
probability that she will visit the cities in alphabetical order?
1
1
1
A)
B)
C) 39,916,800
D)
39,916,800
121
11
85)
86) In a certain lottery, five different numbers between 1 and 31 inclusive are drawn. These are the
winning numbers. To win the lottery, a person must select the correct 5 numbers in the same order
in which they were drawn. What is the probability of winning?
1
1
1
120
A)
B)
C)
D)
120
31!
20,389,320
20,389,320
86)
Identify the given random variable as being discrete or continuous.
87) The number of oil spills occurring off the Alaskan coast
A) Discrete
B) Continuous
88) The pH level in a shampoo
A) Continuous
B) Discrete
11
87)
88)
Find the mean of the given probability distribution.
89)
x P(x)
0 0.19
1 0.11
2 0.30
3 0.06
4 0.34
A) 2.34
B) 2.15
89)
C) 2.44
D) 2.25
90) The number of golf balls ordered by customers of a pro shop has the following probability
distribution.
x
3
6
9 12 15
p(x) 0.14 0.28 0.36 0.12 0.10
A) 5.61
B) 9
C) 9.24
D) 8.28
90)
91) In a certain town, 30% of adults have a college degree. The accompanying table describes the
probability distribution for the number of adults (among 4 randomly selected adults) who have a
college degree.
x
P(x)
0 0.2401
1 0.4116
2 0.2646
3 0.0756
4 0.0081
A) 1.20
B) 1.44
C) 2.00
D) 1.10
91)
92) The probabilities that a batch of 4 computers will contain 0, 1, 2, 3, and 4 defective computers are
0.4521, 0.3970, 0.1307, 0.0191, and 0.0010, respectively. Round answer to the nearest hundredth.
A) 0.62
B) 2.00
C) 0.72
D) 1.17
92)
93) A police department reports that the probabilities that 0, 1, 2, and 3 burglaries will be reported in a
given day are 0.50, 0.43, 0.06, and 0.01, respectively.
A) 1.50
B) 0.58
C) 0.25
D) 1.08
93)
Solve the problem.
94) In a game, you have a 1/29 probability of winning $106 and a 28/29 probability of losing $9. What
is your expected value?
A) -$5.03
B) $3.66
C) -$8.69
D) $12.34
94)
95) A contractor is considering a sale that promises a profit of $35,000 with a probability of 0.7 or a loss
(due to bad weather, strikes, and such) of $6000 with a probability of 0.3. What is the expected
profit?
A) $28,700
B) $24,500
C) $29,000
D) $22,700
95)
96) Suppose you pay $2.00 to roll a fair die with the understanding that you will get back $4.00 for
rolling a 6 or a 5, nothing otherwise. What is your expected value?
A) $4.00
B) $2.00
C) -$0.67
D) -$2.00
96)
12
97) Suppose you buy 1 ticket for $1 out of a lottery of 1,000 tickets where the prize for the one winning
ticket is to be $500. What is your expected value?
A) -$0.40
B) -$1.00
C) $0.00
D) -$0.50
97)
98) The prizes that can be won in a sweepstakes are listed below together with the chances of winning
each one:
$4800 (1 chance in 8300); $1700 (1 chance in 5300); $900 (1 chance in 4600);
$300 (1 chance in 2700).
Find the expected value of the amount won for one entry if the cost of entering is 65 cents.
A) $1.09
B) $0.52
C) $300
D) $0.56
98)
99) The prizes that can be won in a sweepstakes are listed below together with the chances of winning
each one:
$5300 (1 chance in 8100); $2000 (1 chance in 6000); $500 (1 chance in 4400);
$100 (1 chance in 2300).
Find the expected value of the amount won for one entry if the cost to enter is 61 cents.
A) $99.39
B) $1.14
C) $0.49
D) $0.53
99)
Assume that a researcher randomly selects 14 newborn babies and counts the number of girls selected, x. The
probabilities corresponding to the 14 possible values of x are summarized in the given table. Answer the question using
the table.
x(girls)
0
1
2
3
4
Probabilities of Girls
P(x) x(girls) P(x) x(girls)
0.000
5
0.122
10
0.001
6
0.183
11
0.006
7
0.209
12
0.022
8
0.183
13
0.061
9
0.122
14
P(x)
0.061
0.022
0.006
0.001
0.000
100) Find the probability of selecting exactly 8 girls.
A) 0.022
B) 0.183
C) 0.000
D) 0.122
101) Find the probability of selecting exactly 5 girls.
A) 0.061
B) 0.122
C) 0.001
D) 0.022
102) Find the probability of selecting exactly 4 girls.
A) 0.122
B) 0.001
C) 0.061
D) 0.022
103) Find the probability of selecting 9 or more girls.
A) 0.212
B) 0.001
C) 0.061
D) 0.122
104) Find the probability of selecting 12 or more girls.
A) 0.006
B) 0.022
C) 0.007
D) 0.001
105) Find the probability of selecting 2 or more girls.
A) 0.999
B) 0.006
C) 0.994
D) 0.001
13
100)
101)
102)
103)
104)
105)
Answer the question.
106) Assume that there is a 0.15 probability that a basketball playoff series will last four games, a 0.30
probability that it will last five games, a 0.25 probability that it will last six games, and a 0.30
probability that it will last seven games. Is it unusual for a team to win a series in 5 games?
A) No
B) Yes
106)
107) Assume that there is a 0.05 probability that a sports playoff series will last four games, a 0.45
probability that it will last five games, a 0.45 probability that it will last six games, and a 0.05
probability that it will last seven games. Is it unusual for a team to win a series in 7 games?
A) No
B) Yes
107)
108) Suppose that computer literacy among people ages 40 and older is being studied and that the
accompanying tables describes the probability distribution for four randomly selected people,
where x is the number that are computer literate. Is it unusual to find four computer literates
among four randomly selected people?
x Px
0 0.16
1 0.25
2 0.36
3 0.15
4 0.08
A) No
B) Yes
108)
109) Suppose that voting in municipal elections is being studied and that the accompanying tables
describes the probability distribution for four randomly selected people, where x is the number that
voted in the last election. Is it unusual to find four voters among four randomly selected people?
x Px
0 0.23
1 0.32
2 0.26
3 0.15
4 0.04
A) Yes
B) No
109)
110) Suppose that a law enforcement group studying traffic violations determines that the
accompanying table describes the probability distribution for five randomly selected people,
where x is the number that have received a speeding ticket in the last 2 years. Is it unusual to find
no speeders among five randomly selected people?
x Px
0 0.08
1 0.18
2 0.25
3 0.22
4 0.19
5 0.08
A) Yes
B) No
110)
14
Find the indicated probability.
111) A test consists of 10 true/false questions. To pass the test a student must answer at least 8 questions
correctly. If a student guesses on each question, what is the probability that the student will pass
the test?
A) 0.044
B) 0.989
C) 0.055
D) 0.011
111)
112) A machine has 11 identical components which function independently. The probability that a
component will fail is 0.2. The machine will stop working if more than three components fail. Find
the probability that the machine will be working.
A) 0.949
B) 0.111
C) 0.162
D) 0.839
112)
113) In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are
selected at random from the physics majors, that is the probability that no more than 6 belong to
an ethnic minority?
A) 0.9815
B) 0.0547
C) 0.913
D) 0.9846
113)
114) Find the probability of at least 2 girls in 9 births. Assume that male and female births are equally
likely and that the births are independent events.
A) 0.980
B) 0.070
C) 0.020
D) 0.910
114)
115) A company purchases shipments of machine components and uses this acceptance sampling plan:
Randomly select and test 26 components and accept the whole batch if there are fewer than 3
defectives. If a particular shipment of thousands of components actually has a 3% rate of defects,
what is the probability that this whole shipment will be accepted?
A) 0.0348
B) 0.9580
C) 0.5051
D) 0.1408
115)
116) An airline estimates that 92% of people booked on their flights actually show up. If the airline
books 75 people on a flight for which the maximum number is 73, what is the probability that the
number of people who show up will exceed the capacity of the plane?
A) 0.0548
B) 0.0019
C) 0.0145
D) 0.0125
116)
117) In a study, 40% of adults questioned reported that their health was excellent. A researcher wishes
to study the health of people living close to a nuclear power plant. Among 10 adults randomly
selected from this area, only 3 reported that their health was excellent. Find the probability that
when 10 adults are randomly selected, 3 or fewer are in excellent health.
A) 0.2150
B) 0.2687
C) 0.1673
D) 0.3823
117)
118) The participants in a television quiz show are picked from a large pool of applicants with
approximately equal numbers of men and women. Among the last 10 participants there have been
only 2 women. If participants are picked randomly, what is the probability of getting 2 or fewer
women when 10 people are picked?
A) 0.0439
B) 0.0107
C) 0.0537
D) 0.0547
118)
119) A car insurance company has determined that 8% of all drivers were involved in a car accident last
year. Among the 15 drivers living on one particular street, 3 were involved in a car accident last
year. If 15 drivers are randomly selected, what is the probability of getting 3 or more who were
involved in a car accident last year?
A) 0.1130
B) 0.9143
C) 0.0857
D) 0.3993
119)
15
Solve the problem.
120) According to a college survey, 22% of all students work full time. Find the mean for the number of
students who work full time in samples of size 16.
A) 0.22
B) 3.52
C) 4.00
D) 2.75
120)
121) A die is rolled 9 times and the number of times that two shows on the upper face is counted. If this
experiment is repeated many times, find the mean for the number of twos.
A) 3
B) 2.25
C) 1.5
D) 7.5
121)
122) On a multiple choice test with 21 questions, each question has four possible answers, one of which
is correct. For students who guess at all answers, find the mean for the number of correct answers.
A) 5.3
B) 15.8
C) 7
D) 10.5
122)
123) The probability that a radish seed will germinate is 0.7. A gardener plants seeds in batches of 16.
Find the mean for the number of seeds germinating in each batch.
A) 11.36
B) 14.4
C) 11.2
D) 4.8
123)
124) A company manufactures batteries in batches of 5 and there is a 3% rate of defects. Find the mean
number of defects per batch.
A) 0.15
B) 0.155
C) 4.85
D) 0.145
124)
125) The probability that a person has immunity to a particular disease is 0.2. Find the mean number
who have immunity in samples of size 16.
A) 0.2
B) 12.8
C) 8.0
D) 3.2
125)
126) The probability is 0.2 that a person shopping at a certain store will spend less than $20. For groups
of size 13, find the mean number who spend less than $20.
A) 10.4
B) 16.0
C) 4.0
D) 2.6
126)
127) In a certain town, 90 percent of voters are in favor of a given ballot measure and 10 percent are
opposed. For groups of 220 voters, find the mean for the number who oppose the measure.
A) 22
B) 90
C) 10
D) 198
127)
128) The probability of winning a certain lottery is 1/60,547. For people who play 973 times, find the
mean number of wins.
A) 0.000017
B) 0.0010
C) 62.2
D) 0.0161
128)
129) According to a college survey, 22% of all students work full time. Find the standard deviation for
the number of students who work full time in samples of size 16.
A) 1.88
B) 2.75
C) 1.66
D) 3.52
129)
130) A die is rolled 6 times and the number of twos that come up is tallied. If this experiment is
repeated many times, find the standard deviation for the number of twos.
A) 0.833
B) 0.917
C) 0.913
D) 1.22
130)
131) On a multiple choice test with 16 questions, each question has four possible answers, one of which
is correct. For students who guess at all answers, find the standard deviation for the number of
correct answers.
A) 1.732
B) 1.677
C) 1.643
D) 1.697
131)
16
132) The probability that a radish seed will germinate is 0.7. A gardener plants seeds in batches of 5.
Find the standard deviation for the number of seeds germinating in each batch.
A) 1.025
B) 0.917
C) 0.906
D) 1.012
132)
133) A company manufactures batteries in batches of 11 and there is a 3% rate of defects. Find the
standard deviation for the number of defects per batch.
A) 0.566
B) 0.574
C) 0.564
D) 0.539
133)
134) On a multiple choice test with 12 questions, each question has four possible answers, one of which
is correct. For students who guess at all answers, find the variance for the number of correct
answers.
A) 2.16
B) 2.25
C) 1.98
D) 2.063
134)
135) A company manufactures batteries in batches of 18 and there is a 3% rate of defects. Find the
variance for the number of defects per batch.
A) 0.524
B) 0.52
C) 0.495
D) 0.54
135)
136) The probability of winning a certain lottery is 1/78,059. For people who play 955 times, find the
standard deviation for the number of wins.
A) 0.1106
B) 0.1212
C) 0.0122
D) 3.4181
136)
137) In a certain town, 56% of voters favor a given ballot measure. For groups of 35 voters, find the
variance for the number who favor the measure.
A) 74.37
B) 2.94
C) 8.62
D) 19.60
137)
Using the following uniform density curve, answer the question.
138) What is the probability that the random variable has a value greater than 4?
A) 0.450
B) 0.375
C) 0.500
D) 0.625
138)
139) What is the probability that the random variable has a value greater than 1.4?
A) 0.9500
B) 0.8250
C) 0.7750
D) 0.7000
139)
140) What is the probability that the random variable has a value less than 8?
A) 1.000
B) 0.750
C) 1.125
140)
141) What is the probability that the random variable has a value less than 4.1?
A) 0.5125
B) 0.2625
C) 0.3875
D) 0.875
D) 0.6375
142) What is the probability that the random variable has a value between 4.4 and 4.7?
A) 0.0875
B) 0.1625
C) 0.0375
D) 0.2875
17
141)
142)
Assume that the weight loss for the first month of a diet program varies between 6 pounds and 12 pounds, and is spread
evenly over the range of possibilities, so that there is a uniform distribution. Find the probability of the given range of
pounds lost.
143) Between 10.5 pounds and 12 pounds
143)
1
1
3
1
A)
B)
C)
D)
4
2
4
3
If Z is a standard normal variable, find the probability.
144) The probability that Z lies between 0 and 3.01
A) 0.5013
B) 0.1217
C) 0.4987
D) 0.9987
145) The probability that Z lies between -2.41 and 0
A) 0.4920
B) 0.5080
C) 0.0948
D) 0.4910
146) The probability that Z is less than 1.13
A) 0.8485
B) 0.1292
C) 0.8907
D) 0.8708
147) The probability that Z lies between -1.10 and -0.36
A) 0.2237
B) -0.2237
C) 0.4951
D) 0.2239
148) The probability that Z lies between 0.7 and 1.98
A) 0.2181
B) -0.2181
C) 1.7341
D) 0.2175
149) The probability that Z lies between -0.55 and 0.55
A) 0.4176
B) -0.4176
C) -0.9000
D) 0.9000
150) The probability that Z is greater than -1.82
A) 0.4656
B) 0.0344
C) 0.9656
D) -0.0344
151) P(Z > 0.59)
A) 0.2224
B) 0.7224
C) 0.2190
D) 0.2776
152) P(Z < 0.97)
A) 0.8078
B) 0.8315
C) 0.8340
D) 0.1660
153) P(-0.73 < Z < 2.27)
A) 0.2211
B) 0.4884
C) 1.54
D) 0.7557
18
144)
145)
146)
147)
148)
149)
150)
151)
152)
153)
The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of 0°C at
the freezing point of water. Tests on a large sample of these thermometers reveal that at the freezing point of water,
some give readings below 0°C (denoted by negative numbers) and some give readings above 0°C (denoted by positive
numbers). Assume that the mean reading is 0°C and the standard deviation of the readings is 1.00°C. Also assume that
the frequency distribution of errors closely resembles the normal distribution. A thermometer is randomly selected and
tested. Find the temperature reading corresponding to the given information.
154) Find P96, the 96th percentile.
154)
A) 1.82°
B) 1.03°
C) -1.38°
155) Find P40, the 40th percentile.
A) 0.25°
B) -0.25°
156) Find Q3, the third quartile.
A) 0.67°
D) 1.75°
155)
C) 0.57°
D) -0.57°
156)
B) 0.53°
C) -1.3°
D) 0.82°
157) If 9% of the thermometers are rejected because they have readings that are too high, but all other
thermometers are acceptable, find the temperature that separates the rejected thermometers from
the others.
A) 1.26°
B) 1.39°
C) 1.45°
D) 1.34°
157)
158) If 7% of the thermometers are rejected because they have readings that are too low, but all other
thermometers are acceptable, find the temperature that separates the rejected thermometers from
the others.
A) -1.26°
B) -1.39°
C) -1.53°
D) -1.48°
158)
159) A quality control analyst wants to examine thermometers that give readings in the bottom 4%.
Find the reading that separates the bottom 4% from the others.
A) -1.63°
B) -1.48°
C) -1.75°
D) -1.89°
159)
160) A quality control analyst wants to examine thermometers that give readings in the bottom 7%.
Find the reading that separates the bottom 7% from the others.
A) -1.75°
B) -1.63°
C) -1.89°
D) -1.48°
160)
161) If 6.3% of the thermometers are rejected because they have readings that are too high and another
6.3% are rejected because they have readings that are too low, find the two readings that are cutoff
values separating the rejected thermometers from the others.
A) -1.45° , 1.45°
B) -1.53° , 1.53°
C) -1.39° , 1.39°
D) -1.46° , 1.46°
161)
Solve the problem.
162) In one region, the September energy consumption levels for single-family homes are found to be
normally distributed with a mean of 1050 kWh and a standard deviation of 218 kWh. Find P45,
which is the consumption level separating the bottom 45% from the top 55%.
A) 1087.8
B) 1078.3
C) 1148.1
D) 1021.7
163) Scores on a test are normally distributed with a mean of 63.7 and a standard deviation of 10.3. Find
P81, which separates the bottom 81% from the top 19%.
A) 72.8
B) 66.7
C) 0.88
19
162)
D) 0.291
163)
164) A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean
of 200 and a standard deviation of 50. Find P60, the score which separates the lower 60% from the
top 40%.
A) 211.3
B) 187.5
C) 207.8
164)
D) 212.5
165) The amount of rainfall in January in a certain city is normally distributed with a mean of 3.7 inches
and a standard deviation of 0.5 inches. Find the value of the quartile Q1 .
165)
166) Assume that women have heights that are normally distributed with a mean of 63.6 inches and a
standard deviation of 2.5 inches. Find the value of the quartile Q 3 .
166)
167) Scores on an English test are normally distributed with a mean of 30.6 and a standard deviation of
6. Find the score that separates the top 59% from the bottom 41%
A) 27.1
B) 29.2
C) 32.0
D) 34.1
167)
168) Suppose that replacement times for washing machines are normally distributed with a mean of 8.6
years and a standard deviation of 1.6 years. Find the replacement time that separates the top 18%
from the bottom 82%.
A) 8.9 years
B) 10.1 years
C) 9.5 years
D) 7.1 years
168)
169) Human body temperatures are normally distributed with a mean of 98.20°F and a standard
deviation of 0.62°F. Find the temperature that separates the top 7% from the bottom 93%.
A) 97.28°F
B) 98.78°F
C) 98.40°F
D) 99.12°F
169)
170) The weights of certain machine components are normally distributed with a mean of 8.04 g and a
standard deviation of 0.08 g. Find the two weights that separate the top 3% and the bottom 3%.
Theses weights could serve as limits used to identify which components should be rejected.
A) 7.87 g and 8.26 g
B) 8.03 g and 8.05 g
C) 7.89 g and 8.19 g
D) 8.00 g and 8.08 g
170)
171) The serum cholesterol levels for men in one age group are normally distributed with a mean of 178
and a standard deviation of 40.5. All units are in mg/100 mL. Find the two levels that separate the
top 9% and the bottom 9%.
A) 161.4 mg/100mL and 194.6 mg/100mL
B) 107.5 mg/100mL and 248.5 mg/100mL
C) 165.0 mg/100mL and 190.96 mg/100mL
D) 123.7 mg/100mL and 232.3 mg/100mL
171)
A) 3.4
A) 66.1 inches
B) 0.9
C) 3.5
B) 64.3 inches
C) 65.3 inches
D) 4.0
D) 67.8 inches
Find the indicated probability.
172) The diameters of bolts produced by a certain machine are normally distributed with a mean of
0.30 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter
greater than 0.32 inches?
A) 2.28%
B) 47.72%
C) 97.72%
D) 37.45%
173) The incomes of trainees at a local mill are normally distributed with a mean of $1100 and a
standard deviation $150. What percentage of trainees earn less than $900 a month?
A) 9.18%
B) 90.82%
C) 35.31%
D) 40.82%
20
172)
173)
174) The volumes of soda in quart soda bottles are normally distributed with a mean of 32.3 oz and a
standard deviation of 1.2 oz. What is the probability that the volume of soda in a randomly
selected bottle will be less than 32 oz?
A) 0.3821
B) 0.0987
C) 0.5987
D) 0.4013
174)
175) The diameters of pencils produced by a certain machine are normally distributed with a mean of
0.30 inches and a standard deviation of 0.01 inches. What is the probability that the diameter of a
randomly selected pencil will be less than 0.285 inches?
A) 0.0596
B) 0.4332
C) 0.9332
D) 0.0668
175)
176) The weekly salaries of teachers in one state are normally distributed with a mean of $490 and a
standard deviation of $45. What is the probability that a randomly selected teacher earns more
than $525 a week?
A) 0.1003
B) 0.2823
C) 0.2177
D) 0.7823
176)
177) A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean
of 200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a
rating that is between 200 and 275.
A) 0.5
B) 0.9332
C) 0.4332
D) 0.0668
177)
178) In one region, the September energy consumption levels for single-family homes are found to be
normally distributed with a mean of 1050 kWh and a standard deviation of 218 kWh. For a
randomly selected home, find the probability that the September energy consumption level is
between 1100 kWh and 1225 kWh.
A) 0.0910
B) 0.3791
C) 0.1971
D) 0.2881
178)
179) The lengths of human pregnancies are normally distributed with a mean of 268 days and a
standard deviation of 15 days. What is the probability that a pregnancy lasts at least 300 days?
A) 0.4834
B) 0.0166
C) 0.9834
D) 0.0179
179)
180) Assume that the weights of quarters are normally distributed with a mean of 5.67 g and a standard
deviation 0.070 g. A vending machine will only accept coins weighing between 5.48 g and 5.82 g.
What percentage of legal quarters will be rejected?
A) 0.0196%
B) 1.62%
C) 1.96%
D) 2.48%
180)
Solve the problem.
181) The amount of snowfall falling in a certain mountain range is normally distributed with a mean of
89 inches, and a standard deviation of 16 inches. What is the probability that the mean annual
snowfall during 64 randomly picked years will exceed 91.8 inches?
A) 0.4192
B) 0.0026
C) 0.5808
D) 0.0808
181)
182) The annual precipitation amounts in a certain mountain range are normally distributed with a
mean of 99 inches, and a standard deviation of 14 inches. What is the probability that the mean
annual precipitation during 49 randomly picked years will be less than 101.8 inches?
A) 0.5808
B) 0.0808
C) 0.9192
D) 0.4192
182)
183) The weights of the fish in a certain lake are normally distributed with a mean of 11 lb and a
standard deviation of 12. If 16 fish are randomly selected, what is the probability that the mean
weight will be between 8.6 and 14.6 lb?
A) 0.3270
B) 0.6730
C) 0.0968
D) 0.4032
183)
21
184) The scores on a certain test are normally distributed with a mean score of 65 and a standard
deviation of 2. What is the probability that a sample of 90 students will have a mean score of at
least 65.2108?
A) 0.1587
B) 0.3174
C) 0.3413
D) 0.8413
184)
185) A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean
of 200 and a standard deviation of 50. If 40 different applicants are randomly selected, find the
probability that their mean is above 215.
A) 0.1179
B) 0.3821
C) 0.0287
D) 0.4713
185)
186) In one region, the September energy consumption levels for single-family homes are found to be
normally distributed with a mean of 1050 kWh and a standard deviation of 218 kWh. If 50
different homes are randomly selected, find the probability that their mean energy consumption
level for September is greater than 1075 kWh.
A) 0.2910
B) 0.4562
C) 0.2090
D) 0.0438
186)
187) Assume that women's heights are normally distributed with a mean of 63.6 inches and a standard
deviation of 2.5 inches. If 90 women are randomly selected, find the probability that they have a
mean height between 62.9 inches and 64.0 inches.
A) 0.0424
B) 0.7248
C) 0.1739
D) 0.9318
187)
188) Suppose that replacement times for washing machines are normally distributed with a mean of
9.3 years and a standard deviation of 1.1 years. Find the probability that 70 randomly selected
washing machines will have a mean replacement time less than 9.1 years.
A) 0.4286
B) 0.0643
C) 0.4357
D) 0.0714
188)
189) Human body temperatures are normally distributed with a mean of 98.20°F and a standard
deviation of 0.62°F. If 19 people are randomly selected, find the probability that their mean body
temperature will be less than 98.50°F.
A) 0.3343
B) 0.0833
C) 0.9826
D) 0.4826
189)
190) For women aged 18-24, systolic blood pressures (in mm Hg) are normally distributed with a mean
of 114.8 and a standard deviation of 13.1. If 23 women aged 18-24 are randomly selected, find the
probability that their mean systolic blood pressure is between 119 and 122.
A) 0.0577
B) 0.3343
C) 0.0833
D) 0.9341
190)
191) A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 Chevrolet
Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics
are randomly selected, find the probability that their mean rebuild time exceeds 8.7 hours.
A) 0.1946
B) 0.1285
C) 0.1346
D) 0.1469
191)
192) A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 Chevrolet
Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics
are randomly selected, find the probability that their mean rebuild time exceeds 9.1 hours.
A) 0.1046
B) 0.1285
C) 0.0069
D) 0.0046
192)
193) A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 Chevrolet
Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics
are randomly selected, find the probability that their mean rebuild time exceeds 7.7 hours.
A) 0.8531
B) 0.9931
C) 0.9712
D) 0.9634
193)
22
194) A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 Chevrolet
Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics
are randomly selected, find the probability that their mean rebuild time exceeds 8.1 hours.
A) 0.8531
B) 0.7285
C) 0.8457
D) 0.9146
194)
195) A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 Chevrolet
Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics
are randomly selected, find the probability that their mean rebuild time is less than 7.6 hours.
A) 0.0103
B) 0.0008
C) 0.0036
D) 0.0025
195)
196) A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 Chevrolet
Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics
are randomly selected, find the probability that their mean rebuild time is less than 8.9 hours.
A) 0.9589
B) 0.9756
C) 0.4276
D) 0.9608
196)
197) A final exam in Math 160 has a mean of 73 with standard deviation 7.8. If 24 students are
randomly selected, find the probability that the mean of their test scores is greater than 78.
A) 0.0103
B) 0.8962
C) 0.0036
D) 0.0008
197)
198) A final exam in Math 160 has a mean of 73 with standard deviation 7.8. If 24 students are
randomly selected, find the probability that the mean of their test scores is greater than 71.
A) 0.5036
B) 0.0008
C) 0.8962
D) 0.9012
198)
199) A final exam in Math 160 has a mean of 73 with standard deviation 7.8. If 24 students are
randomly selected, find the probability that the mean of their test scores is less than 76.
A) 0.8962
B) 0.9203
C) 0.9699
D) 0.0301
199)
200) A final exam in Math 160 has a mean of 73 with standard deviation 7.8. If 24 students are
randomly selected, find the probability that the mean of their test scores is less than 70.
A) 0.9699
B) 0.0301
C) 0.0278
D) 0.1006
200)
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EXTRA CREDIT: Answer questions on a seperate paper.
Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution.
201) A multiple choice test consists of 60 questions. Each question has 4 possible answers of
201)
which one is correct. If all answers are random guesses, estimate the probability of getting
at least 20% correct.
202) A certain question on a test is answered correctly by 22% of the respondents. Estimate the
probability that among the next 150 responses there will be at most 40 correct answers.
202)
203) A product is manufactured in batches of 120 and the overall rate of defects is 5%. Estimate
the probability that a randomly selected batch contains more than 6 defects.
203)
204) In one county, the conviction rate for speeding is 85%. Estimate the probability that of the
next 100 speeding summonses issued, there will be at least 90 convictions.
204)
205) The probability that a radish seed will germinate is 0.7. Estimate the probability that of 140
randomly selected seeds, exactly 100 will germinate.
205)
206) Two percent of hair dryers produced in a certain plant are defective. Estimate the
probability that of 10,000 randomly selected hair dryers, exactly 225 are defective.
206)
207) Two percent of hair dryers produced in a certain plant are defective. Estimate the
probability that of 10,000 randomly selected hair dryers, at least 219 are defective.
207)
208) A coin is tossed 20 times. A person, who claims to have extrasensory perception, is asked
to predict the outcome of each flip in advance. She predicts correctly on 14 tosses. What is
the probability of being correct 14 or more times by guessing? Does this probability seem
to verify her claim?
208)
209) Find the probability that in 200 tosses of a fair die, we will obtain at exactly 30 fives.
209)
210) Merta reports that 74% of its trains are on time. A check of 60 randomly selected trains
shows that 38 of them arrived on time. Find the probability that among the 60 trains, 38 or
fewer arrive on time. Based on the result, does it seem plausible that the "on-time" rate of
74% could be correct?
210)
24