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An automobile manufacturer is concerned about a fault in the braking mechanism of a particular model. The fault can, on rare occasions, cause a catastrophe at high speed. The distribution of the number of cars per year that will experience the catastrophe is a Poisson random variable with λ = 4.5. (a) What is the probability that at most 3 cars per year will experience a catastrophe? (b) What is the probability that more than 2 cars per year will experience a catastrophe? Click here to view page 1 of the table of Poisson probability sums. Click here to view page 2 of the table of Poisson probability sums.

An automobile manufacturer is concerned about a fault in the braking mechanism of a particular model. The fault can, on rare occasions, cause a catastrophe at high speed. The distribution of the number of cars per year that will experience the catastrophe is a Poisson random variable with λ = 4.5. (a) What is the probability that at most 3 cars per year will experience a catastrophe? (b) What is the probability that more than 2 cars per year will experience a catastrophe? Click here to view page 1 of the table of Poisson probability sums. Click here to view page 2 of the table of Poisson probability sums.

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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3 T 0.1 0.2 0.3 0.4 0.6 0.7 0 0.9048 0.8187 0.7408 0.6703 0.6065 0.5488 0.4966 1 0.9953 0.9825 0.9631 2 4 5 6 1² 10 11 12 13 14 15 16 0.9998 1.0000 1² 0.1 Poisson Probability Sums p(x;μ) Σ p(x;µ) 2-0 1.0 0.8 0.9 0.4493 0.4066 0.9384 0.9098 0.8781 0.8442 0.8088 0.7725 0.9371 0.9989 0.9964 0.9921 0.9856 0.9769 0.9659 0.9526 0.9999 0.9997 0.9992 0.9982 0.9966 0.9942 0.9909 0.9865 1.0000 1.0000 0.9999 0.9998 0.9996 0.9992 0.9986 0.9977 1.0000 1.0000 1.0000 0.9999 0.9998 0.9997 1.0000 1.0000 1.0000 0.8 0.7 0.9 0.2 Tº fl 1.0 2.0 1.5 2.5 3.0 3.5 4.0 4.5 5.0 0 0.3679 0.2231 0.1353 0.0821 0.0498 0.0302 0.0183 0.0111 0.0067 1 0.7358 0.5578 0.4060 0.2873 0.1991 0.1359 0.0916 0.0611 0.0404 2 0.9197 0.8088 0.6767 0.5438 0.4232 0.3208 0.2381 0.1736 0.1247 3 0.9810 0.9344 0.8571 0.7576 0.6472 0.5366 0.4335 0.3423 0.2650 4 0.9963 0.9814 0.9473 0.8912 0.8153 0.7254 0.6288 0.5321 0.4405 0.9834 0.9580 0.9161 0.8576 0.7851 0.7029 0.6160 6 0.9999 0.9991 0.9955 0.9858 0.9665 0.9347 0.8893 0.8311 0.7622 1.0000 0.9998 0.9989 0.9958 0.9881 0.9733 0.9489 0.9134 0.8666 1.0000 0.9998 0.9989 0.9962 0.9901 0.9786 0.9597 0.9319 1.0000 0.9997 0.9989 0.9967 0.9919 0.9829 0.9682 0.9999 0.9997 0.9990 0.9972 0.9933 0.9863 1.0000 5 0.9994 0.9955 7 8 9 0.3 1.5 " 0.5 0.4 2.0 2.5 0.5 P 0.9999 1.0000 0.6 3.0 f 0.9997 0.9991 0.9976 0.9945 0.9999 0.9997 0.9992 0.9980 0.9999 0.9997 1.0000 0.9999 1.0000 0.9993 0.9998 1.0000 0.9999 1.0000 5.0 3.5 4.0 4.5 1 1 Poisson Probability Sums p(x;μ) 5.5 0.1649 fl 6.0 6.5 7.0 7.5 8.0 8.5 9.0 0 0.0041 0.0025 0.0015 0.0009 0.0006 0.0003 0.0002 0.0001 1 0.0266 0.0174 0.0113 0.0073 0.0047 0.0030 0.0019 0.0012 2 0.0884 0.0620 0.0430 0.0296 0.0203 0.0138 0.0093 0.0062 3 0.2017 0.1512 0.1118 0.0818 0.0591 0.0424 0.0301 0.0212 4 0.3575 0.2851 0.2237 0.1730 0.1321 0.0996 0.0744 0.0550 5 0.5289 0.4457 0.3690 0.3007 0.2414 0.1912 0.1496 0.1157 0.6860 0.6063 0.5265 0.4497 0.3782 0.3134 0.2562 0.2068 0.8095 0.7440 0.6728 0.5987 0.5246 0.4530 0.3856 0.3239 0.2687 0.8944 0.8472 0.7916 0.7291 0.6620 0.5925 0.5231 0.4557 0.3918 0.9462 0.9161 0.8774 0.8305 0.7764 0.7166 0.6530 0.5874 0.5218 0.9747 0.9574 0.9332 0.9015 0.8622 0.8159 0.7634 0.7060 0.6453 11 0.9890 0.9799 0.9661 0.9467 0.9208 0.8881 0.8487 0.8030 0.7520 12 0.9955 0.9912 0.9840 0.9730 0.9573 0.9362 0.9091 0.8758 0.8364 13 0.9983 0.9964 0.9929 0.9872 0.9784 0.9658 0.9486 0.9261 0.8981 14 0.9994 0.9986 0.9970 0.9943 0.9897 0.9827 0.9726 0.9585 0.9400 15 0.9998 0.9995 0.9988 0.9976 0.9954 0.9918 0.9862 0.9780 0.9665 0.9998 0.9996 0.9990 0.9980 0.9963 0.9934 0.9889 0.9823 0.9998 0.9996 0.9992 0.9984 0.9970 0.9947 0.9911 0.9999 0.9999 0.9997 0.9993 0.9987 0.9976 0.9957 1.0000 1.0000 0.9999 0.9997 0.9995 0.9989 0.9980 0.9999 0.9998 0.9996 0.9991 1.0000 0.9999 0.9998 0.9996 1.0000 0.9999 0.9999 0.9999 16 0.9999 1.0000 0.9999 1.0000 17 18 19 20 1.0000 1.0000 9.5 els 6 7 8 9 10 21 22 23 24 P 5.5 6.0 6.5 7.0 2=0 7.5 fl 8.0 8.5 9.0 9.5 0.0001 0.0008 0.0042 0.0149 0.0403 0.0885
Transcribed Image Text:3 T 0.1 0.2 0.3 0.4 0.6 0.7 0 0.9048 0.8187 0.7408 0.6703 0.6065 0.5488 0.4966 1 0.9953 0.9825 0.9631 2 4 5 6 1² 10 11 12 13 14 15 16 0.9998 1.0000 1² 0.1 Poisson Probability Sums p(x;μ) Σ p(x;µ) 2-0 1.0 0.8 0.9 0.4493 0.4066 0.9384 0.9098 0.8781 0.8442 0.8088 0.7725 0.9371 0.9989 0.9964 0.9921 0.9856 0.9769 0.9659 0.9526 0.9999 0.9997 0.9992 0.9982 0.9966 0.9942 0.9909 0.9865 1.0000 1.0000 0.9999 0.9998 0.9996 0.9992 0.9986 0.9977 1.0000 1.0000 1.0000 0.9999 0.9998 0.9997 1.0000 1.0000 1.0000 0.8 0.7 0.9 0.2 Tº fl 1.0 2.0 1.5 2.5 3.0 3.5 4.0 4.5 5.0 0 0.3679 0.2231 0.1353 0.0821 0.0498 0.0302 0.0183 0.0111 0.0067 1 0.7358 0.5578 0.4060 0.2873 0.1991 0.1359 0.0916 0.0611 0.0404 2 0.9197 0.8088 0.6767 0.5438 0.4232 0.3208 0.2381 0.1736 0.1247 3 0.9810 0.9344 0.8571 0.7576 0.6472 0.5366 0.4335 0.3423 0.2650 4 0.9963 0.9814 0.9473 0.8912 0.8153 0.7254 0.6288 0.5321 0.4405 0.9834 0.9580 0.9161 0.8576 0.7851 0.7029 0.6160 6 0.9999 0.9991 0.9955 0.9858 0.9665 0.9347 0.8893 0.8311 0.7622 1.0000 0.9998 0.9989 0.9958 0.9881 0.9733 0.9489 0.9134 0.8666 1.0000 0.9998 0.9989 0.9962 0.9901 0.9786 0.9597 0.9319 1.0000 0.9997 0.9989 0.9967 0.9919 0.9829 0.9682 0.9999 0.9997 0.9990 0.9972 0.9933 0.9863 1.0000 5 0.9994 0.9955 7 8 9 0.3 1.5 " 0.5 0.4 2.0 2.5 0.5 P 0.9999 1.0000 0.6 3.0 f 0.9997 0.9991 0.9976 0.9945 0.9999 0.9997 0.9992 0.9980 0.9999 0.9997 1.0000 0.9999 1.0000 0.9993 0.9998 1.0000 0.9999 1.0000 5.0 3.5 4.0 4.5 1 1 Poisson Probability Sums p(x;μ) 5.5 0.1649 fl 6.0 6.5 7.0 7.5 8.0 8.5 9.0 0 0.0041 0.0025 0.0015 0.0009 0.0006 0.0003 0.0002 0.0001 1 0.0266 0.0174 0.0113 0.0073 0.0047 0.0030 0.0019 0.0012 2 0.0884 0.0620 0.0430 0.0296 0.0203 0.0138 0.0093 0.0062 3 0.2017 0.1512 0.1118 0.0818 0.0591 0.0424 0.0301 0.0212 4 0.3575 0.2851 0.2237 0.1730 0.1321 0.0996 0.0744 0.0550 5 0.5289 0.4457 0.3690 0.3007 0.2414 0.1912 0.1496 0.1157 0.6860 0.6063 0.5265 0.4497 0.3782 0.3134 0.2562 0.2068 0.8095 0.7440 0.6728 0.5987 0.5246 0.4530 0.3856 0.3239 0.2687 0.8944 0.8472 0.7916 0.7291 0.6620 0.5925 0.5231 0.4557 0.3918 0.9462 0.9161 0.8774 0.8305 0.7764 0.7166 0.6530 0.5874 0.5218 0.9747 0.9574 0.9332 0.9015 0.8622 0.8159 0.7634 0.7060 0.6453 11 0.9890 0.9799 0.9661 0.9467 0.9208 0.8881 0.8487 0.8030 0.7520 12 0.9955 0.9912 0.9840 0.9730 0.9573 0.9362 0.9091 0.8758 0.8364 13 0.9983 0.9964 0.9929 0.9872 0.9784 0.9658 0.9486 0.9261 0.8981 14 0.9994 0.9986 0.9970 0.9943 0.9897 0.9827 0.9726 0.9585 0.9400 15 0.9998 0.9995 0.9988 0.9976 0.9954 0.9918 0.9862 0.9780 0.9665 0.9998 0.9996 0.9990 0.9980 0.9963 0.9934 0.9889 0.9823 0.9998 0.9996 0.9992 0.9984 0.9970 0.9947 0.9911 0.9999 0.9999 0.9997 0.9993 0.9987 0.9976 0.9957 1.0000 1.0000 0.9999 0.9997 0.9995 0.9989 0.9980 0.9999 0.9998 0.9996 0.9991 1.0000 0.9999 0.9998 0.9996 1.0000 0.9999 0.9999 0.9999 16 0.9999 1.0000 0.9999 1.0000 17 18 19 20 1.0000 1.0000 9.5 els 6 7 8 9 10 21 22 23 24 P 5.5 6.0 6.5 7.0 2=0 7.5 fl 8.0 8.5 9.0 9.5 0.0001 0.0008 0.0042 0.0149 0.0403 0.0885
An automobile manufacturer is concerned about a fault in the braking mechanism of a particular model. The fault can, on rare occasions, cause a catastrophe at high speed. The distribution of the number of cars per year that will experience the catastrophe is a Poisson random variable with λ = 4.5. (a) What is the probability that at most 3 cars per year will experience a catastrophe? (b) What is the probability that more than 2 cars per year will experience a catastrophe? Click here to view page 1 of the table of Poisson probability sums. Click here to view page 2 of the table of Poisson probability sums. (a) The probability that at most 3 cars per year will experience a catastrophe is (Round to four decimal places as needed.) (b) The probability that more than 2 cars per year will experience a catastrophe is (Round to four decimal places as needed.)
Transcribed Image Text:An automobile manufacturer is concerned about a fault in the braking mechanism of a particular model. The fault can, on rare occasions, cause a catastrophe at high speed. The distribution of the number of cars per year that will experience the catastrophe is a Poisson random variable with λ = 4.5. (a) What is the probability that at most 3 cars per year will experience a catastrophe? (b) What is the probability that more than 2 cars per year will experience a catastrophe? Click here to view page 1 of the table of Poisson probability sums. Click here to view page 2 of the table of Poisson probability sums. (a) The probability that at most 3 cars per year will experience a catastrophe is (Round to four decimal places as needed.) (b) The probability that more than 2 cars per year will experience a catastrophe is (Round to four decimal places as needed.)
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