A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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A manufacturer knows that on average 20% of toasters produced require repairs within 1 year after they are sold. When 18 toasters are randomly selected, find the smallest number x and largest number y such that (a) the
Transcribed Image Text:Table A.1 (continued) Binomial Probability Sums b(x;n, p)
n T 0.10
0.20
17 0 0.1668 0.0225
1 0.4818 0.1182
2 0.7618 0.3096 0.1637
3 0.9174 0.5489 0.3530 0.2019
0.9779 0.7582 0.5739 0.3887
4
5
0.9953 0.8943 0.7653
6
0.9992
8
1.0000
0.0047
0.9623 0.8929 0.7752 0.4478 0.1662 0.0348 0.0032 0.0001
7 0.9999 0.9891 0.9598 0.8954 0.6405 0.3145 0.0919 0.0127 0.0005
0.9974 0.9876 0.9597 0.8011 0.5000 0.1989 0.0403 0.0026 0.0000
0.9995 0.9969 0.9873 0.9081 0.6855 0.3595 0.1046 0.0109 0.0001
0.9999 0.9994 0.9968 0.9652 0.8338 0.5522 0.2248 0.0377 0.0008
1.0000 0.9999 0.9993 0.9894 0.9283 0.7361 0.4032 0.1057
1.0000 0.9999 0.9975 0.9755 0.8740 0.6113 0.2418 0.0221
1.0000 0.9995 0.9936 0.9536 0.7981 0.4511 0.0826
0.9999 0.9988 0.9877 0.9226 0.6904 0.2382
1.0000 0.9999 0.9979 0.9807 0.8818 0.5182
0.9998 0.9977 0.9775 0.8332
1.0000 1.0000 1.0000 1.0000
1.0000
9
10
11
12
n
13
14
15
16
17
18 0 0.1501
1
2
3
10
11
12
13
14
15
16
17
18
0.0180 0.0056
0.0016
0.0001
0.0000
0.4503 0.0991 0.0395
0.0142 0.0013
0.0001
0.7338 0.2713 0.1353 0.0600 0.0082
0.0007
0.9018 0.5010 0.3057 0.1646 0.0328 0.0038
4
0.9718
5 0.9936 0.8671 0.7175
6
0.7164 0.5187 0.3327 0.0942 0.0154 0.0013 0.0000
0.5344 0.2088 0.0481 0.0058 0.0003
0.9988 0.9487 0.8610 0.7217 0.3743
0.9837 0.9431 0.8593 0.5634
0.9957 0.9807
7
0.9998
8
1.0000
9
0.9991
0.9998
1.0000
P 0.10
0.40
0.25 0.30
0.0075 0.0023 0.0002
0.0501
0.0193 0.0021
0.20
x=0
0.50
0.0000
0.0001 0.0000
0.0774 0.0123 0.0012 0.0001
0.25
0.30
0.60
0.0464 0.0064 0.0005 0.0000
0.1260 0.0245 0.0025 0.0001
0.5968 0.2639 0.0717 0.0106 0.0007 0.0000
0.40
0.70
P
0.1189 0.0203 0.0014 0.0000
0.2403 0.0576 0.0061 0.0002
0.4073 0.1347 0.0210 0.0009
0.9998 0.9986
1.0000 0.9997
1.0000
0.9404 0.7368
0.9946 0.9790 0.8653 0.5927 0.2632 0.0596 0.0043 0.0000
0.9988 0.9939 0.9424 0.7597 0.4366 0.1407 0.0163 0.0002
0.9797 0.8811 0.6257 0.2783 0.0513 0.0012
0.9942 0.9519 0.7912 0.4656 0.1329 0.0064
0.9987 0.9846 0.9058 0.6673 0.2836 0.0282
0.9998 0.9962 0.9672 0.8354 0.4990 0.0982
1.0000 0.9993 0.9918 0.9400 0.7287 0.2662
0.9858 0.9009
0.5497
0.9999 0.9987
1.0000 0.9999
0.9984 0.9820
0.8499
1.0000 1.0000 1.0000
1.0000
0.60 0.70
0.80
0.90
0.50
0.0000
0.0002
0.80
0.90
Transcribed Image Text:Table A.1 (continued) Binomial Probability Sums b(x; n, p)
n
0.20
0.25 0.30 0.40
19 0
0.1351
0.0144
0.0042
0.0011
0.0001
1
0.4203
0.0829
0.0310
0.0104
0.0008
2 0.7054
0.2369
0.1113 0.0462 0.0055
3 0.8850
0.4551
0.2631 0.1332 0.0230
0.6733 0.4654 0.2822 0.0696
5 0.9914 0.8369 0.6678 0.4739 0.1629
4 0.9648
P 0.10
n
7
8
9
10
11
12
13
14
15
16
17
18
19
10
11
12
13
14
15
16
17
18
19
20
r
0.0835 0.0116 0.0006
0.1796 0.0352 0.0028 0.0000
0.0885 0.0105 0.0003
0.5000 0.1861 0.0326
6 0.9983 0.9324 0.8251 0.6655 0.3081
0.9997 0.9767 0.9225 0.8180 0.4878
1.0000 0.9933 0.9713 0.9161 0.6675 0.3238
0.9984 0.9911 0.9674 0.8139
0.0016
0.9997 0.9977 0.9895 0.9115 0.6762 0.3325 0.0839 0.0067 0.0000
1.0000 0.9995 0.9972 0.9648 0.8204 0.5122 0.1820 0.0233 0.0003
0.9999 0.9994 0.9884 0.9165 0.6919 0.3345 0.0676 0.0017
1.0000 0.9999 0.9969 0.9682 0.8371 0.5261 0.1631 0.0086
1.0000 0.9994 0.9904 0.9304 0.7178 0.3267
0.9999 0.9978 0.9770 0.8668 0.5449
1.0000
0.0352
0.1150
0.9996
0.9945 0.9538 0.7631
0.2946
1.0000
0.9992 0.9896 0.9171 0.5797
0.9999 0.9989 0.9856 0.8649
1.0000 1.0000
1.0000
1.0000
0.0115
0.3917 0.0692
0.6769 0.2061 0.0913
2=0
0.0032
0.0243 0.0076
20 0 0.1216
1
0.0005 0.0000
2
0.0355 0.0036 0.0002
0.0000
3 0.8670 0.4114 0.2252 0.1071 0.0160 0.0013
4 0.9568 0.6296 0.4148 0.2375 0.0510 0.0059 0.0003
5 0.9887 0.8042 0.6172
6
0.4164
0.9976 0.9133 0.7858 0.6080
0.9996 0.9679 0.8982 0.7723
0.9999
9 1.0000
7
8
0.10
0.0008 0.0000
P
0.20 0.25 0.30
0.50
0.40
0.60
P
0.0000
0.0004 0.0000
0.0022 0.0001
0.0096 0.0006 0.0000
0.0318 0.0031 0.0001
0.1256 0.0207 0.0016 0.0000
0.2500
0.0577 0.0065 0.0003
0.1316 0.0210 0.0013 0.0000
0.2517 0.0565 0.0051 0.0001
0.4119 0.1275 0.0171 0.0006
0.4159
0.9900 0.9591 0.8867 0.5956
0.9974 0.9861 0.9520 0.7553
0.9994 0.9961 0.9829 0.8725 0.5881 0.2447 0.0480 0.0026 0.0000
0.9999 0.9991 0.9949 0.9435 0.7483 0.4044 0.1133 0.0100 0.0001
1.0000 0.9998 0.9987 0.9790 0.8684 0.5841 0.2277 0.0321 0.0004
1.0000 0.9997 0.9935 0.9423 0.7500 0.3920 0.0867 0.0024
1.0000 0.9984 0.9793 0.8744 0.5836 0.1958 0.0113
0.9997 0.9941 0.9490 0.7625 0.3704 0.0432
1.0000 0.9987 0.9840 0.8929 0.5886 0.1330
0.9998 0.9964 0.9645 0.7939 0.3231
1.0000 0.9995 0.9924 0.9308 0.6083
1.0000 0.9992 0.9885 0.8784
1.0000 1.0000 1.0000
0.70 0.80 0.90
0.70 0.80
0.50
0.90
0.60
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