Data Set 3 --Lincolnville School District Bus Data
ID
10
396
122
751
279
500
520
759
714
875
600
953
101
358
29
365
162
686
370
887
464
948
678
481
43
704
814
39
699
75
693
989
982
321
724
732
880
193
884
57
Manufacturer
Keiser
Thompson
Bluebird
Keiser
Bluebird
Bluebird
Bluebird
Keiser
Bluebird
Bluebird
Bluebird
Bluebird
Bluebird
Bluebird
Bluebird
Keiser
Keiser
Bluebird
Keiser
Bluebird
Bluebird
Keiser
Keiser
Keiser
Bluebird
Bluebird
Bluebird
Bluebird
Bluebird
Bluebird
Keiser
Keiser
Bluebird
Bluebird
Keiser
Keiser
Keiser
Thompson
Bluebird
Bluebird
Engine Type
(0=diesel)
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
Capacity
14
14
55
14
55
55
55
55
42
55
55
55
55
55
55
55
55
55
55
55
55
42
55
6
55
55
55
55
55
55
55
55
55
42
42
42
55
14
55
55
Maintenance
Cost
4646
1072
9394
1078
1008
5329
4794
3952
3742
4376
4832
5160
1955
2775
5352
3065
3143
1569
7766
3743
2540
4342
3361
3097
8263
4218
2028
5821
9069
3011
9193
4795
505
2732
3754
4640
8410
5922
4364
3190
Age
5
2
10
2
2
5
10
8
7
9
10
10
4
6
6
6
3
3
8
8
3
9
7
3
9
8
4
6
9
6
9
9
1
6
8
9
9
11
9
7
Odometer
Miles
54375
21858
116580
22444
22672
50765
119130
87872
73703
97947
119860
117700
41096
70086
69438
63384
31266
34674
86528
93672
34530
97956
75229
34362
102969
83424
40824
69444
98307
71970
101889
106605
10276
70122
91968
101196
97065
128711
92457
79240
731
61
135
833
671
692
200
754
540
660
353
482
398
984
977
705
767
326
120
554
695
9
861
603
156
427
883
168
954
768
490
725
45
38
314
507
40
918
387
418
Bluebird
Keiser
Bluebird
Thompson
Thompson
Bluebird
Bluebird
Keiser
Bluebird
Bluebird
Keiser
Bluebird
Thompson
Bluebird
Bluebird
Keiser
Keiser
Bluebird
Keiser
Bluebird
Bluebird
Keiser
Bluebird
Keiser
Thompson
Keiser
Bluebird
Thompson
Bluebird
Bluebird
Bluebird
Bluebird
Keiser
Keiser
Thompson
Bluebird
Bluebird
Bluebird
Bluebird
Bluebird
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
1
0
42
55
55
14
14
55
55
14
55
55
55
55
6
55
55
42
55
55
42
42
55
55
55
14
14
55
55
14
42
42
55
55
55
14
6
55
55
55
55
55
3213
4139
3560
3920
6733
3770
5168
7380
3656
6213
4279
10575
4752
3809
3769
2152
2985
4563
4723
1826
1061
3527
9669
2116
6212
6927
1881
7004
5284
3173
10133
2356
3124
5976
5408
3690
9573
2470
6863
4513
6
9
7
8
8
8
10
14
4
6
4
10
9
8
7
4
6
9
10
4
2
4
10
4
12
7
2
7
10
7
10
5
6
6
11
7
10
5
8
9
68526
103536
76426
90968
89792
93248
103700
146860
45284
64434
45744
116534
95922
87664
79422
47596
71538
107343
110320
44604
23152
46848
106040
44384
140460
73423
20742
83006
101000
71778
106240
57065
60102
61662
128117
72849
118470
53620
89960
104715
Miles
11973
11969
11967
11948
11925
11922
11896
11889
11837
11814
11800
11798
11789
11782
11781
11778
11757
11707
11704
11698
11698
11691
11668
11662
11615
11610
11576
11533
11518
11462
11461
11418
11359
11358
11344
11342
11336
11248
11231
11222
Variables
ID = Bus identification number
Manufacturer = Source of the bus (Bluebird, Keiser, or Thompson)
Engine type = If the engine is diesel then engine type = 0; if the engine is gasolin
Capacity = number of seats on the bus
Maintenance cost = dollars spent to maintain a bus last year
Age = number of years since the bus left the manufacturer
Odometer Miles = total number of miles traveled by a bus
Miles = number of miles traveled since last maintenance
11168
11148
11127
11112
11100
11048
11018
11003
10945
10911
10902
10802
10802
10760
10759
10755
10726
10724
10674
10662
10633
10591
10551
10518
10473
10355
10344
10315
10235
10227
10210
10209
10167
10140
10128
10095
10081
10075
10055
10000
ine type = 0; if the engine is gasoline, then engine type = 1)
Balance
1756
748
1501
1831
1622
1886
740
1593
1169
2125
1554
1474
1913
1218
1006
2215
137
167
343
2557
2276
1494
2144
1995
1053
1526
1120
1838
1746
1616
1958
634
580
1320
1675
789
1735
1784
1326
2051
1044
1885
1790
765
1645
32
1266
890
2204
2409
1338
ATM
Services
13
9
10
10
14
17
6
10
6
18
12
12
6
10
12
20
7
5
7
20
15
11
17
10
8
8
8
7
11
10
6
2
4
4
6
8
12
11
16
14
7
10
11
4
6
2
11
7
14
16
14
4
2
1
4
6
3
3
8
4
6
6
7
5
3
4
3
2
4
2
7
4
2
3
7
4
4
6
5
2
4
2
7
1
5
7
4
7
5
8
4
5
6
4
3
9
0
7
1
5
8
4
Debit
Interest
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
1
1
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
City
2
1
1
3
4
1
3
1
4
2
3
1
1
1
1
4
3
4
1
4
3
1
3
2
3
2
3
3
2
2
2
4
1
1
2
4
3
1
3
4
1
2
3
4
4
3
4
1
2
2
2
2076
1708
2138
2375
1455
1487
1125
1989
2156
12
13
18
12
9
8
6
12
14
5
3
5
4
5
4
4
3
5
1
1
0
0
1
1
1
0
1
0
0
1
0
1
0
0
1
0
2
1
4
2
3
4
2
2
2
Team
League
Opened
Team Salary
Attendance
Arizona
National
1998
65,80
2080145
Atlanta
National
1996
89,60
2001392
Baltimore
American
1992
118,90
2281202
Boston
American
1912
168,70
2880694
National
1914
117,20
2959812
American
1991
110,70
1755810
Cincinnati
National
2003
117,70
2419506
Cleveland
American
1994
87,70
1388905
Colorado
National
1995
98,30
2506789
Detroit
American
2000
172,80
2726048
Houston
American
2000
69,10
2153585
Kansas City
American
1973
112,90
2708549
LA Angels
American
1966
146,40
3012765
LA Dodgers
National
1962
230,40
3764815
Miami
National
2012
84,60
1752235
National
American
2001
2010
98,70
108,30
2542558
2220054
National
2009
100,10
2569753
NY Yankees
American
2009
213,50
3193795
Oakland
American
1966
80,80
1768175
Philadelphia
National
2004
133,00
1831080
Pittsburgh
National
2001
85,90
2498596
San Diego
National
2004
126,60
2459742
San Francisco
National
2000
166,50
3375882
Seattle
American
1999
123,20
2193581
St. Louis
National
2006
120,30
3520889
Tampa Bay
American
1990
74,80
1287054
Texas
American
1994
144,80
2491875
Toronto
American
1989
116,40
2794891
National
2008
174,50
2619843
Chicago Cubs
Chicago White Sox
Milwaukee
Minnesota
NY Mets
Washington
Wins
ERA
BA
HR
Year
79
4,04
0,264
154
2000
67
4,41
0,251
100
2001
81
4,05
0,25
217
2002
78
4,31
0,265
161
2003
97
3,36
0,244
171
2004
76
3,98
0,25
136
2005
64
4,33
0,248
167
2006
81
3,67
0,256
141
2007
68
5,04
0,265
186
2008
74
4,64
0,27
151
2009
86
3,57
0,25
230
2010
95
3,73
0,269
139
2011
85
3,94
0,246
176
2012
92
3,44
0,25
187
2013
71
4,02
0,26
120
2014
68
83
4,28
4,07
0,251
0,247
145
156
2015
90
3,43
0,244
177
87
4,05
0,251
212
68
4,14
0,251
146
63
4,69
0,249
130
98
3,21
0,26
140
74
4,09
0,243
148
84
3,72
0,267
136
76
4,16
0,249
198
100
2,94
0,253
137
80
3,74
0,252
167
88
2,24
0,257
172
93
3,8
0,269
232
83
3,62
0,251
177
2016
Average Salary
1,99
2,26
2,38
2,56
2,49
2,63
2,87
2,94
3,15
3,24
3,3
3,31
3,44
3,65
3,95
4,25
4,4
Team = Team’s name
League = American or National League
Year Opened = First year the team’s stadium was used
Team Salary = Total team salary expressed in millions of dollars
Attendance = Total number of people attending regular season games
Wins = Number of regular season games won
ERA = Team earned run average
BA = Team batting average
HR = Team home runs
Year = Year of operation
Average salary = Average annual player salary in dollars
compute the mean and
the standard deviation of this distribution.
b. Create a probability distribution for the number of bathrooms. Compute the mean
and the standard deviation of this distribution.
71. FILE Refer to the Baseball 2016 data. Compute the mean number of home runs per
game. To do this, first find the mean number of home runs per team for 2016. Next,
divide this value by 162 (a season comprises 162 games). Then multiply by 2 because
there are two teams in each game. Use the Poisson distribution to estimate the number
of home runs that will be hit in a game. Find the probability that:
a. There are no home runs in a game.
b. There are two home runs in a game.
c. There are at least four home runs in a game.
DATA
JL.
e
É
w
225 of 890
DISCRETE PROBABILITY DISTRIBUTIONS
O freo
45. An auditor for Health Maintenance Services of Georgia reports 40% of policyholders
years or older submit a claim during the year. Fifteen policyholders are randomly
selected for company records.
a. How many of the policyholders would you expect to have filed a claim within the last
year?
b. What is the probability
that 10 of the selected policyholders submitted a claim last year?
c. What is the probability that 10 or more of the selected policyholders submitted a
claim last year?
d. What is the probability that more than 10 of the selected policyholders submitted a
claim last year?
46. Tire and Auto Supply is considering a 2-for-1 stock split. Before the transaction is final-
ized, at least two-thirds of the 1.200 company stockholders must approve the proposal
To evaluate the likelihood the proposal will be approved, the CFO selected a sample of
18 stockholders. He contacted each and found 14 approved of the proposed split. What
is the likelihood of this event, assuming two-thirds of the stockholders approve?
47. A federal study reported that 7.5% of the U.S. workforce has a drug problem. A drug
enforcement official for the state of Indiana wished to investigate this statement. In her
sample of 20 employed workers
a. How many would you expect to have a drug problem? What is the standard deviation?
din nroblem?
tual number. Comment on the accuracy of your estimate.
b. The mean team salary was $121 million, with a standard deviation of $40.0 million.
Use the normal distribution to estimate the number of teams with a team salary of
more than $ 100 million. Compare that estimate with the actual number. Comment on
the accuracy of the estimate.
76. Refer to the Lincolnville School District bus data.
a. Refer to the maintenance cost variable. The mean maintenance cost for last year is
$4,552 with a standard deviation of $2332. Estimate the number of buses with a
maintenance cost of more than $6,000. Compare that with the actual number. Create
a frequency distribution of maintenance cost. Is the distribution normally distributed?
b. Refer to the variable on the number of miles driven since the last maintenance. The
mean is 11,121 and the
standard deviation is 617 miles. Estimate the number of
buses traveling more than 11.500 miles since the last maintenance. Compare that
number with the actual value. Create a frequency distribution of miles since mainte-
nance cost. Is the distribution normally distributed?
OF CHAPTERS 5-7
section consider methods of dealing with uncertainty. In Chapter 5, we describe the concept of prob-
is a value between 0 and 1 that expresses the likelihood a particular event will occur. We also looked
alate probabilities using rules of addition and multiplication; presented principles of counting, including
combinations, and described situations for using Bayes' theorem.
es discrete probability distributions. Discrete probability distributions list all possible outcomes of an exper-
ability associated with each outcome. We describe three discrete probability distributions: the binomial
pergeometric distribution and the Poisson distribution. The requirements for the binomial distribution are
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