Homework Help is Here – Start Your Trial Now!
Math
Probability
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 probability that at least x of them will require repairs is less than 0.58; ​(b) the probability that at least y of them will not require repairs is greater than 0.84.

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 probability that at least x of them will require repairs is less than 0.58; ​(b) the probability that at least y of them will not require repairs is greater than 0.84.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 10E
See similar textbooks
icon
Related questions
Question
100%

I need help with this:

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 probability that at least x of them will require repairs is less than 0.58; ​(b) the probability that at least y of them will not require repairs is greater than 0.84.

Table A.1 (continued) Binomial Probability Sums b(a; n, p) 9 10 11 12 n 13 14 n r 0.10 0.20 19 0 0.1351 0.0144 0.4203 0.0829 1 0.1113 0.0462 0.0055 0.0004 0.0000 2 0.7054 0.2369 3 0.8850 0.4551 0.9648 0.6733 0.2631 0.1332 0.0230 0.0022 0.0001 4 0.0000 7 0.9997 8 1.0000 0.4654 0.2822 0.0696 0.0096 0.0006 5 0.9914 0.8369 0.6678 0.4739 0.1629 0.0318 0.0031 0.0001 6 0.9983 0.9324 0.8251 0.6655 0.3081 0.0835 0.0116 0.0006 0.9767 0.9225 0.8180 0.4878 0.1796 0.9933 0.9713 0.9161 0.6675 0.3238 0.9984 0.9911 0.9674 0.8139 0.9997 0.9977 0.9895 0.9115 1.0000 0.9995 0.9972 0.9648 0.8204 0.9999 0.9994 0.9884 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 0.0352 0.9999 0.9978 0.9770 0.8668 0.5449 0.1150 1.0000 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 0.0352 0.0028 0.0000 0.0885 0.0105 0.0003 0.5000 0.1861 0.0326 0.0016 0.6762 0.3325 0.0839 0.0067 0.0000 0.5122 0.1820 0.0233 0.0003 0.9165 0.6919 0.3345 0.0676 15 16 17 18 19 20 0 10 11 12 13 14 15 16 17 18 19 20 r 0.10 r=0 0.25 0.30 0.40 0.0042 0.0011 0.0001 0.0310 0.0104 0.0008 0.0000 0.1216 0.0115 0.0032 0.0008 0.0000 1 0.3917 0.0692 0.0243 0.0076 0.0005 0.0000 2 0.0002 0.6769 0.2061 0.0913 0.0355 0.0036 0.8670 0.4114 0.2252 0.1071 0.0160 0.0013 0.0000 4 0.0510 0.0059 0.0003 0.9568 0.6296 0.4148 0.2375 0.9887 0.8042 0.6172 5 0.1256 0.0207 0.0016 0.0000 6 7 0.9996 8 0.9999 0.0000 9 1.0000 0.4164 0.9976 0.9133 0.7858 0.6080 0.2500 0.0577 0.0065 0.0003 0.9679 0.8982 0.7723 0.4159 0.1316 0.0210 0.0013 0.9900 0.9591 0.8867 0.5956 0.2517 0.0565 0.0051 0.0001 0.9974 0.9861 0.9520 0.7553 0.4119 0.1275 0.0171 0.0006 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 0.9984 0.9793 0.8744 0.5836 0.1958 0.9997 0.9941 0.9490 0.7625 0.3704 1.0000 1.0000 0.0113 0.0432 0.9987 0.9840 0.8929 0.5886 0.1330 0.3231 0.9998 1.0000 0.6083 0.8784 1.0000 0.90 0.20 0.25 P 0.30 0.40 0.50 P 0.60 0.50 0.70 0.80 0.9964 0.9645 0.7939 0.9995 0.9924 0.9308 0.60 1.0000 0.9992 0.9885 1.0000 1.0000 0.70 0.80 0.90
Transcribed Image Text:Table A.1 (continued) Binomial Probability Sums b(a; n, p) 9 10 11 12 n 13 14 n r 0.10 0.20 19 0 0.1351 0.0144 0.4203 0.0829 1 0.1113 0.0462 0.0055 0.0004 0.0000 2 0.7054 0.2369 3 0.8850 0.4551 0.9648 0.6733 0.2631 0.1332 0.0230 0.0022 0.0001 4 0.0000 7 0.9997 8 1.0000 0.4654 0.2822 0.0696 0.0096 0.0006 5 0.9914 0.8369 0.6678 0.4739 0.1629 0.0318 0.0031 0.0001 6 0.9983 0.9324 0.8251 0.6655 0.3081 0.0835 0.0116 0.0006 0.9767 0.9225 0.8180 0.4878 0.1796 0.9933 0.9713 0.9161 0.6675 0.3238 0.9984 0.9911 0.9674 0.8139 0.9997 0.9977 0.9895 0.9115 1.0000 0.9995 0.9972 0.9648 0.8204 0.9999 0.9994 0.9884 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 0.0352 0.9999 0.9978 0.9770 0.8668 0.5449 0.1150 1.0000 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 0.0352 0.0028 0.0000 0.0885 0.0105 0.0003 0.5000 0.1861 0.0326 0.0016 0.6762 0.3325 0.0839 0.0067 0.0000 0.5122 0.1820 0.0233 0.0003 0.9165 0.6919 0.3345 0.0676 15 16 17 18 19 20 0 10 11 12 13 14 15 16 17 18 19 20 r 0.10 r=0 0.25 0.30 0.40 0.0042 0.0011 0.0001 0.0310 0.0104 0.0008 0.0000 0.1216 0.0115 0.0032 0.0008 0.0000 1 0.3917 0.0692 0.0243 0.0076 0.0005 0.0000 2 0.0002 0.6769 0.2061 0.0913 0.0355 0.0036 0.8670 0.4114 0.2252 0.1071 0.0160 0.0013 0.0000 4 0.0510 0.0059 0.0003 0.9568 0.6296 0.4148 0.2375 0.9887 0.8042 0.6172 5 0.1256 0.0207 0.0016 0.0000 6 7 0.9996 8 0.9999 0.0000 9 1.0000 0.4164 0.9976 0.9133 0.7858 0.6080 0.2500 0.0577 0.0065 0.0003 0.9679 0.8982 0.7723 0.4159 0.1316 0.0210 0.0013 0.9900 0.9591 0.8867 0.5956 0.2517 0.0565 0.0051 0.0001 0.9974 0.9861 0.9520 0.7553 0.4119 0.1275 0.0171 0.0006 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 0.9984 0.9793 0.8744 0.5836 0.1958 0.9997 0.9941 0.9490 0.7625 0.3704 1.0000 1.0000 0.0113 0.0432 0.9987 0.9840 0.8929 0.5886 0.1330 0.3231 0.9998 1.0000 0.6083 0.8784 1.0000 0.90 0.20 0.25 P 0.30 0.40 0.50 P 0.60 0.50 0.70 0.80 0.9964 0.9645 0.7939 0.9995 0.9924 0.9308 0.60 1.0000 0.9992 0.9885 1.0000 1.0000 0.70 0.80 0.90
Table A.1 (continued) Binomial Probability Sums b(x; n, p) n r 0.10 17 0 n 7 8 9 10 11 0.20 0.1668 0.0225 0.0075 1 0.4818 0.1182 0.0501 2 0.7618 0.3096 0.1637 0.0774 0.0123 0.0012 0.0001 3 0.9174 0.5489 0.3530 0.2019 0.0464 0.0064 0.0005 0.0000 0.1260 0.0245 0.0025 0.0001 4 0.9779 0.7582 0.5739 0.3887 5 0.9953 0.8943 0.7653 0.5968 6 0.9992 0.9623 0.8929 0.9999 0.9891 0.9598 1.0000 12 13 14 15 16 17 18 0 0.1501 0.0180 10 11 12 13 14 15 16 17 18 r 0.10 0.25 0.30 0.40 0.50 0.0023 0.0002 0.0000 0.9974 0.9876 0.9597 0.9995 0.9969 0.9873 0.9999 0.9994 0.9999 1.0000 1.0000 0.20 x=0 0.25 0.0056 0.4503 0.0991 0.0395 1 2 0.7338 0.2713 0.1353 0.0600 3 0.9018 0.5010 0.3057 0.1646 4 5 0.0000 0.5634 0.9718 0.7164 0.5187 0.3327 0.0942 0.0154 0.0013 0.0000 0.9936 0.8671 0.7175 0.5344 0.2088 0.0481 0.0058 0.0003 6 0.9988 0.9487 0.8610 0.7217 0.3743 0.1189 0.0203 0.0014 7 0.9998 0.9837 0.9431 0.8593 0.0576 0.0061 0.0002 0.9957 0.9807 0.9404 0.9991 0.9946 0.9790 0.9998 0.9988 0.9939 1.0000 0.9998 0.9986 1.0000 0.2403 0.4073 0.1347 0.0210 0.0009 8 1.0000 0.7368 9 0.8653 0.5927 0.2632 0.0596 0.0043 0.0000 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 0.9999 0.9987 0.9858 0.9009 0.5497 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 0.0193 0.0021 0.0001 0.0000 P 0.0016 0.0001 0.0142 0.0013 0.9997 1.0000 0.30 0.2639 0.0717 0.0106 0.0007 0.0000 0.7752 0.4478 0.1662 0.0348 0.0032 0.0001 0.8954 0.6405 0.3145 0.0919 0.0127 0.0005 0.8011 0.5000 0.1989 0.0403 0.0026 0.0000 0.9081 0.6855 0.3595 0.1046 0.0109 0.0001 0.9968 0.9652 0.8338 0.5522 0.2248 0.0377 0.0008 0.9993 0.9894 0.9283 0.7361 0.4032 0.1057 0.0047 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 1.0000 0.9998 0.9977 0.9775 0.8332 1.0000 1.0000 1.0000 1.0000 0.60 0.0000 0.0001 0.0082 0.0007 0.0000 0.0328 0.0038 0.0002 0.40 0.70 P 0.50 0.80 0.90
Transcribed Image Text:Table A.1 (continued) Binomial Probability Sums b(x; n, p) n r 0.10 17 0 n 7 8 9 10 11 0.20 0.1668 0.0225 0.0075 1 0.4818 0.1182 0.0501 2 0.7618 0.3096 0.1637 0.0774 0.0123 0.0012 0.0001 3 0.9174 0.5489 0.3530 0.2019 0.0464 0.0064 0.0005 0.0000 0.1260 0.0245 0.0025 0.0001 4 0.9779 0.7582 0.5739 0.3887 5 0.9953 0.8943 0.7653 0.5968 6 0.9992 0.9623 0.8929 0.9999 0.9891 0.9598 1.0000 12 13 14 15 16 17 18 0 0.1501 0.0180 10 11 12 13 14 15 16 17 18 r 0.10 0.25 0.30 0.40 0.50 0.0023 0.0002 0.0000 0.9974 0.9876 0.9597 0.9995 0.9969 0.9873 0.9999 0.9994 0.9999 1.0000 1.0000 0.20 x=0 0.25 0.0056 0.4503 0.0991 0.0395 1 2 0.7338 0.2713 0.1353 0.0600 3 0.9018 0.5010 0.3057 0.1646 4 5 0.0000 0.5634 0.9718 0.7164 0.5187 0.3327 0.0942 0.0154 0.0013 0.0000 0.9936 0.8671 0.7175 0.5344 0.2088 0.0481 0.0058 0.0003 6 0.9988 0.9487 0.8610 0.7217 0.3743 0.1189 0.0203 0.0014 7 0.9998 0.9837 0.9431 0.8593 0.0576 0.0061 0.0002 0.9957 0.9807 0.9404 0.9991 0.9946 0.9790 0.9998 0.9988 0.9939 1.0000 0.9998 0.9986 1.0000 0.2403 0.4073 0.1347 0.0210 0.0009 8 1.0000 0.7368 9 0.8653 0.5927 0.2632 0.0596 0.0043 0.0000 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 0.9999 0.9987 0.9858 0.9009 0.5497 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 0.0193 0.0021 0.0001 0.0000 P 0.0016 0.0001 0.0142 0.0013 0.9997 1.0000 0.30 0.2639 0.0717 0.0106 0.0007 0.0000 0.7752 0.4478 0.1662 0.0348 0.0032 0.0001 0.8954 0.6405 0.3145 0.0919 0.0127 0.0005 0.8011 0.5000 0.1989 0.0403 0.0026 0.0000 0.9081 0.6855 0.3595 0.1046 0.0109 0.0001 0.9968 0.9652 0.8338 0.5522 0.2248 0.0377 0.0008 0.9993 0.9894 0.9283 0.7361 0.4032 0.1057 0.0047 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 1.0000 0.9998 0.9977 0.9775 0.8332 1.0000 1.0000 1.0000 1.0000 0.60 0.0000 0.0001 0.0082 0.0007 0.0000 0.0328 0.0038 0.0002 0.40 0.70 P 0.50 0.80 0.90
Expert Solution
steps

Step by step

Solved in 4 steps with 20 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781337282291
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
SEE MORE TEXTBOOKS