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According to Chemical Engineering Progress (November 1990), approximately 30% of all pipework failures in chemical plants are caused by operator error. Complete parts (a) through (c). Click here to view page 1 of the table of binomial probability sums. Click here to view page 2 of the table of binomial probability sums. (a) What is the probability that out of the next 20 pipework failures at least 10 are due to operator error? The probability is (Round to four decimal places as needed.) (b) What is the probability that no more than 4 out of 20 such failures are due to operator error? The probability is (Round to four decimal places as needed.) (c) Suppose, for a particular plant, that out of the random sample of 20 such failures, exactly 7 are due to operator error. Do you feel that the 30% figure stated above applies to this plant? Explain. If 30% of all pipework failures in the chemical plant were caused by operator error, then the probability that exactly 7 of the failures in the sample are due to operator error would be. Since this probability is than 0.05, this reasonable. a rare event. The 30% figure is is not cimal places as needed.)

According to Chemical Engineering Progress (November 1990), approximately 30% of all pipework failures in chemical plants are caused by operator error. Complete parts (a) through (c). Click here to view page 1 of the table of binomial probability sums. Click here to view page 2 of the table of binomial probability sums. (a) What is the probability that out of the next 20 pipework failures at least 10 are due to operator error? The probability is (Round to four decimal places as needed.) (b) What is the probability that no more than 4 out of 20 such failures are due to operator error? The probability is (Round to four decimal places as needed.) (c) Suppose, for a particular plant, that out of the random sample of 20 such failures, exactly 7 are due to operator error. Do you feel that the 30% figure stated above applies to this plant? Explain. If 30% of all pipework failures in the chemical plant were caused by operator error, then the probability that exactly 7 of the failures in the sample are due to operator error would be. Since this probability is than 0.05, this reasonable. a rare event. The 30% figure is is not cimal places as needed.)

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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If 30​% of all pipework failures in the chemical plant were caused by operator​ error, then the probability that exactly

7 of the failures in the sample are due to operator error would be_______. Since the probability is (greater or less) than 0.05, this ( is or is not) a rare event. The 30% figure (seems or does not seem) reasonable.
 
(Round to four decimal places)
n 19 20 1 2 8 9 10 11 12 13 14 15 16 17 18 19 0.0104 0.0008 0.0000 3 0.8850 0.4551 0.2631 0.1332 0.4654 0.2822 4 0.9648 0.6733 6 0.9983 0.9324 0.8251 0.0462 0.0055 0.0004 0.0000 0.0230 0.0022 0.0001 0.0696 0.0096 0.0006 0.0000 5 0.9914 0.8369 0.6678 0.4739 0.1629 0.0318 0.0031 0.0001 0.6655 0.3081 0.0835 0.0116 0.0006 0.9997 0.9767 0.9225 0.8180 0.4878 0.1796 0.0352 0.0028 0.0000 1.0000 0.9933 0.9713 0.9161 0.6675 0.3238 0.0885 0.0105 0.0003 0.9984 0.9911 0.9674 0.8139 0.5000 0.1861 0.0326 0.0016 0.9997 0.9977 0.9895 0.9115 0.6762 0.3325 0.0839 0.0067 0.9995 1.0000 0.9972 0.9648 0.8204 0.5122 0.1820 0.0233 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 0.0000 0.0003 0.0352 0.1150 0.2946 1.0000 0.9994 0.9904 0.9304 0.7178 0.3267 0.8668 0.9999 0.9978 0.9770 0.5449 1.0000 0.9996 0.9945 0.9538 0.7631 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 4 5 6 0.10 0.20 0.25 0.30 0.40 0.1351 0.0144 0.0042 0.0011 0.0001 0.4203 0.0829 0.0310 0.7054 0.2369 0.1113 13 14 15 16 17 18 19 20 Binomial Probability Sums 0 0.1216 0.0115 0.0032 0.0008 1 0.0000 0.3917 0.0692 0.0243 0.0076 0.0005 0.6769 0.2061 0.0913 0.0355 0.0036 2 3 0.8670 0.4114 0.2252 0.1071 0.0160 0.0013 0.0000 0.9568 0.6296 0.4148 0.2375 0.0510 0.0059 0.0003 0.9887 0.8042 0.6172 0.4164 0.1256 0.0207 0.0016 0.0000 2/12/24, 11:22 AM https://mylab.pearson.com/Student/PlayerTest.aspx?testid-260840041&centerwin-yes 72 r 0.10 0.20 b(x; n, p) 0.9976 0.9133 0.7858 0.6080 0.2500 0.0577 0.0065 0.0003 8 0.9999 9 10 11 12 0.9996 0.9679 0.8982 0.7723 0.4159 0.1316 0.0210 0.0013 0.0000 0.9900 0.9591 0.8867 0.5956 0.2517 0.0565 0.0051 0.0001 1.0000 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 1.0000 0.9998 0.9987 0.9790 0.8684 0.5841 0.2277 0.0321 1.0000 0.9997 0.9935 0.9423 0.7500 0.3920 0.0867 1.0000 0.9984 0.9793 0.8744 0.5836 0.1958 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 0.0001 0.0004 0.0024 0.0113 0.25 0.30 0.50 0.40 0.60 0.70 P 0.0000 0.0002 Binomial Probability Sums, page 2 0.80 0.50 0.60 0.70 0.90 0.80 0.90 ở «e 3 4 ¡Ai n T 17 0 1 n 0.10 0.20 0.25 0.30 0.40 0.50 0.1668 0.0225 0.0075 0.0023 0.0002 0.0000 0.4818 0.1182 0.0501 0.0193 0.0021 0.0001 0.0000 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 4 0.9779 0.7582 0.5739 0.3887 0.1260 0.0245 0.0025 0.0001 0.9953 0.8943 0.7653 0.5968 0.2639 0.0717 0.0106 0.0007 0.0000 0.9992 0.9623 0.8929 0.7752 0.4478 0.1662 0.0348 0.0032 0.0001 0.9999 0.9891 0.9598 0.8954 0.6405 0.3145 0.0919 0.0127 0.0005 1.0000 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 0.0008 0.0377 1.0000 0.9999 0.9993 0.9894 0.9283 0.7361 0.4032 0.1057 0.0047 1.0000 0.9999 0.9975 0.9755 0.8740 0.6113 0.2418 0.0221 1.0000 0.9936 0.9995 0.7981 0.9536 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 5 6 7 8 9 10 11 12 13 14 4567 15 16 17 18 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 T Binomial Probability Sums b(x; n,p) 0.10 0.20 0.25 Р 0.1501 0.0180 0.0056 0.0016 0.0001 0.0002 0.0013 0.0000 0.0058 0.0003 0.0203 0.0014 0.0000 0.0576 0.0061 0.0002 0.1347 0.0210 0.0009 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 0.0000 0.9018 0.5010 0.3057 0.1646 0.0328 0.0038 0.9718 0.7164 0.5187 0.3327 0.0942 0.0154 0.9936 0.8671 0.7175 0.5344 0.2088 0.0481 0.9988 0.9487 0.8610 0.7217 0.3743 0.1189 0.9998 0.9837 0.9431 0.8593 0.5634 0.2403 1.0000 0.9957 0.9807 0.9404 0.7368 0.4073 0.9991 0.9946 0.9790 0.8653 0.5927 0.2632 0.0596 0.0043 0.0000 0.9998 0.9988 0.9939 0.9424 0.7597 0.4366 0.1407 0.0163 0.0002 1.0000 0.9998 0.9986 0.9797 0.8811 0.6257 0.2783 0.0513 0.0012 1.0000 0.9997 0.9942 0.9519 0.7912 0.4656 0.1329 0.0064 1.0000 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 0.30 0.40 0.60 0.50 0.70 0.80 0.90 0.60 0.70 0.80 0.90
Transcribed Image Text:n 19 20 1 2 8 9 10 11 12 13 14 15 16 17 18 19 0.0104 0.0008 0.0000 3 0.8850 0.4551 0.2631 0.1332 0.4654 0.2822 4 0.9648 0.6733 6 0.9983 0.9324 0.8251 0.0462 0.0055 0.0004 0.0000 0.0230 0.0022 0.0001 0.0696 0.0096 0.0006 0.0000 5 0.9914 0.8369 0.6678 0.4739 0.1629 0.0318 0.0031 0.0001 0.6655 0.3081 0.0835 0.0116 0.0006 0.9997 0.9767 0.9225 0.8180 0.4878 0.1796 0.0352 0.0028 0.0000 1.0000 0.9933 0.9713 0.9161 0.6675 0.3238 0.0885 0.0105 0.0003 0.9984 0.9911 0.9674 0.8139 0.5000 0.1861 0.0326 0.0016 0.9997 0.9977 0.9895 0.9115 0.6762 0.3325 0.0839 0.0067 0.9995 1.0000 0.9972 0.9648 0.8204 0.5122 0.1820 0.0233 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 0.0000 0.0003 0.0352 0.1150 0.2946 1.0000 0.9994 0.9904 0.9304 0.7178 0.3267 0.8668 0.9999 0.9978 0.9770 0.5449 1.0000 0.9996 0.9945 0.9538 0.7631 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 4 5 6 0.10 0.20 0.25 0.30 0.40 0.1351 0.0144 0.0042 0.0011 0.0001 0.4203 0.0829 0.0310 0.7054 0.2369 0.1113 13 14 15 16 17 18 19 20 Binomial Probability Sums 0 0.1216 0.0115 0.0032 0.0008 1 0.0000 0.3917 0.0692 0.0243 0.0076 0.0005 0.6769 0.2061 0.0913 0.0355 0.0036 2 3 0.8670 0.4114 0.2252 0.1071 0.0160 0.0013 0.0000 0.9568 0.6296 0.4148 0.2375 0.0510 0.0059 0.0003 0.9887 0.8042 0.6172 0.4164 0.1256 0.0207 0.0016 0.0000 2/12/24, 11:22 AM https://mylab.pearson.com/Student/PlayerTest.aspx?testid-260840041&centerwin-yes 72 r 0.10 0.20 b(x; n, p) 0.9976 0.9133 0.7858 0.6080 0.2500 0.0577 0.0065 0.0003 8 0.9999 9 10 11 12 0.9996 0.9679 0.8982 0.7723 0.4159 0.1316 0.0210 0.0013 0.0000 0.9900 0.9591 0.8867 0.5956 0.2517 0.0565 0.0051 0.0001 1.0000 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 1.0000 0.9998 0.9987 0.9790 0.8684 0.5841 0.2277 0.0321 1.0000 0.9997 0.9935 0.9423 0.7500 0.3920 0.0867 1.0000 0.9984 0.9793 0.8744 0.5836 0.1958 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 0.0001 0.0004 0.0024 0.0113 0.25 0.30 0.50 0.40 0.60 0.70 P 0.0000 0.0002 Binomial Probability Sums, page 2 0.80 0.50 0.60 0.70 0.90 0.80 0.90 ở «e 3 4 ¡Ai n T 17 0 1 n 0.10 0.20 0.25 0.30 0.40 0.50 0.1668 0.0225 0.0075 0.0023 0.0002 0.0000 0.4818 0.1182 0.0501 0.0193 0.0021 0.0001 0.0000 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 4 0.9779 0.7582 0.5739 0.3887 0.1260 0.0245 0.0025 0.0001 0.9953 0.8943 0.7653 0.5968 0.2639 0.0717 0.0106 0.0007 0.0000 0.9992 0.9623 0.8929 0.7752 0.4478 0.1662 0.0348 0.0032 0.0001 0.9999 0.9891 0.9598 0.8954 0.6405 0.3145 0.0919 0.0127 0.0005 1.0000 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 0.0008 0.0377 1.0000 0.9999 0.9993 0.9894 0.9283 0.7361 0.4032 0.1057 0.0047 1.0000 0.9999 0.9975 0.9755 0.8740 0.6113 0.2418 0.0221 1.0000 0.9936 0.9995 0.7981 0.9536 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 5 6 7 8 9 10 11 12 13 14 4567 15 16 17 18 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 T Binomial Probability Sums b(x; n,p) 0.10 0.20 0.25 Р 0.1501 0.0180 0.0056 0.0016 0.0001 0.0002 0.0013 0.0000 0.0058 0.0003 0.0203 0.0014 0.0000 0.0576 0.0061 0.0002 0.1347 0.0210 0.0009 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 0.0000 0.9018 0.5010 0.3057 0.1646 0.0328 0.0038 0.9718 0.7164 0.5187 0.3327 0.0942 0.0154 0.9936 0.8671 0.7175 0.5344 0.2088 0.0481 0.9988 0.9487 0.8610 0.7217 0.3743 0.1189 0.9998 0.9837 0.9431 0.8593 0.5634 0.2403 1.0000 0.9957 0.9807 0.9404 0.7368 0.4073 0.9991 0.9946 0.9790 0.8653 0.5927 0.2632 0.0596 0.0043 0.0000 0.9998 0.9988 0.9939 0.9424 0.7597 0.4366 0.1407 0.0163 0.0002 1.0000 0.9998 0.9986 0.9797 0.8811 0.6257 0.2783 0.0513 0.0012 1.0000 0.9997 0.9942 0.9519 0.7912 0.4656 0.1329 0.0064 1.0000 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 0.30 0.40 0.60 0.50 0.70 0.80 0.90 0.60 0.70 0.80 0.90
According to Chemical Engineering Progress (November 1990), approximately 30% of all pipework failures in chemical plants are caused by operator error. Complete parts (a) through (c). Click here to view page 1 of the table of binomial probability sums. Click here to view page 2 of the table of binomial probability sums. (a) What is the probability that out of the next 20 pipework failures at least 10 are due to operator error? The probability is (Round to four decimal places as needed.) (b) What is the probability that no more than 4 out of 20 such failures are due to operator error? The probability is (Round to four decimal places as needed.) (c) Suppose, for a particular plant, that out of the random sample of 20 such failures, exactly 7 are due to operator error. Do you feel that the 30% figure stated above applies to this plant? Explain. If 30% of all pipework failures in the chemical plant were caused by operator error, then the probability that exactly 7 of the failures in the sample are due to operator error would be. Since this probability is than 0.05, this reasonable. a rare event. The 30% figure is is not cimal places as needed.)
Transcribed Image Text:According to Chemical Engineering Progress (November 1990), approximately 30% of all pipework failures in chemical plants are caused by operator error. Complete parts (a) through (c). Click here to view page 1 of the table of binomial probability sums. Click here to view page 2 of the table of binomial probability sums. (a) What is the probability that out of the next 20 pipework failures at least 10 are due to operator error? The probability is (Round to four decimal places as needed.) (b) What is the probability that no more than 4 out of 20 such failures are due to operator error? The probability is (Round to four decimal places as needed.) (c) Suppose, for a particular plant, that out of the random sample of 20 such failures, exactly 7 are due to operator error. Do you feel that the 30% figure stated above applies to this plant? Explain. If 30% of all pipework failures in the chemical plant were caused by operator error, then the probability that exactly 7 of the failures in the sample are due to operator error would be. Since this probability is than 0.05, this reasonable. a rare event. The 30% figure is is not cimal places as needed.)
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