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 = 7.5. (a) What is the probability that at most 5 cars per year will experience a catastrophe? (b) What is the probability that more than 1 car per year will experience a catastrophe?
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 = 7.5. (a) What is the probability that at most 5 cars per year will experience a catastrophe? (b) What is the probability that more than 1 car per year will experience a catastrophe?
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...
Related questions
Question
100%
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 = 7.5.
(a) What is the
(b) What is the probability that more than 1 car per year will experience a catastrophe?
Transcribed Image Text:6
0.6860 0.6063
7 0.8095 0.7440
8 0.8944 0.8472
9 0.9462 0.9161
0.9747 0.9574
10
T
5.5
6.0
6.5
7.0
8.0
0 0.0041
0.0025 0.0015
0.0009
0.0006 0.0003
2
0.0062
1 0.0266 0.0174 0.0113 0.0073 0.0047 0.0030
0.0884 0.0620 0.0430 0.0296 0.0203 0.0138 0.0093
0.2017 0.1512 0.1118 0.0818 0.0591 0.0424 0.0301
0.2851 0.2237 0.1730 0.1321 0.0996 0.0744 0.0550
0.4457 0.3690 0.3007 0.2414
3
4 0.3575
0.0212
5
0.5289
0.1912
0.1496
0.1157
16 0.9999 0.9998
0.9999
1.0000
17
1.0000
18
19
20
11
0.9890 0.9799 0.9661
12
0.9955 0.9912
0.9840
13
0.9983 0.9964
0.9929
14 0.9994 0.9986 0.9970
15
0.9998 0.9995
0.9988
21
22
23
24
P
Poisson Probability Sums p(x;p)
5.5
6.0
0.4497 0.3782
0.5265
0.6728
0.7916 0.7291
0.5987
0.8774
0.8305
0.9332
0.9015
0.9467
0.9730
0.9872
0.9943
0.9976
0.9996
0.9990
0.9998 0.9996
0.9999 0.9999
1.0000 1.0000
6.5
2=0
fl
7.5
7.0
0.9208
0.9573
0.9784
0.9897
0.9954
0.2068
0.5246
0.4530
0.3856 0.3239
0.6620
0.5925
0.5231 0.4557
0.7764 0.7166 0.6530 0.5874
0.8622
0.8159
0.7634 0.7060
8.5
9.0
0.0002
0.0001
0.0019 0.0012
0.3134 0.2562
7.5
8.0
0.8881
0.9362 0.9091 0.8758
0.9658 0.9486 0.9261
0.9827 0.9726 0.9585
0.9400
0.9918 0.9862 0.9780 0.9665
0.8487 0.8030 0.7520
0.8364
0.8981
0.9947
0.9980 0.9963 0.9934 0.9889
0.9992 0.9984 0.9970
0.9997 0.9993
0.9999 0.9997
0.9987 0.9976
0.9957
0.9995 0.9989
0.9980
0.9999
0.9998 0.9996 0.9991
1.0000
0.9999
1.0000
9.5
0.0001
0.0008
0.0042
0.0149
0.0403
0.0885
8.5
0.1649
0.2687
0.3918
0.5218
0.6453
0.9998
0.9999
1.0000
9.0
0.9823
0.9911
0.9996
0.9999
0.9999
1.0000
9.5
Transcribed Image Text:T
T
0.1
0.2
0.3
0.4
0.6
0.7
0.8
0 0.9048 0.8187
0.7408
0.6065 0.5488
0.4966 0.4493
1
0.9953
0.9825
0.9631
0.8442
0.8088
2
0.9526
0.9371
3
0.6703
0.9384 0.9098 0.8781
0.9989 0.9964 0.9921 0.9856 0.9769 0.9659
0.9999 0.9997 0.9992 0.9982 0.9966 0.9942 0.9909
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
0.9865
4
5
6
1.0000
1.0000
1.0000
0.7
0.8
0.9
67890 128
4 0.9963
5
10
11
T
1.0
1.5
0
0.3679
0.2231
1
0.7358
0.5578
2
0.9197
0.8088
3 0.9810 0.9344
13
14
0.9998
1.0000
15
16
0.1
T
Poisson Probability Sums Σ p(x;μ)
2=0
0.2
1.0
0.9814 0.9473
0.9955
0.9834
0.9994
0.9999 0.9991
1.0000 0.9998
1.0000
0.3
1.5
2.0
0.1353
0.4060
0.6767
0.8571
0.4
2.0
"
0.5
0.9955
0.9858
0.9989 0.9958
0.9998 0.9989
1.0000
0.5
"
2.5
fl
3.0
2.5
0.0821
0.0498
0.2873
0.1991
0.5438
0.4232
0.7576 0.6472
0.8912 0.8153
0.9580 0.9161 0.8576
3.5
4.0
4.5
5.0
0.0302 0.0183 0.0111 0.0067
0.1359 0.0916
0.0404
0.0611
0.3208 0.2381 0.1736
0.1247
0.5366 0.4335 0.3423
0.2650
0.7254 0.6288 0.5321
0.7851
0.9347 0.8893 0.8311
0.7029
0.9489 0.9134
0.9733
0.9901 0.9786 0.9597
0.9665
0.9881
0.9962
0.9997 0.9989 0.9967
0.9999 0.9997 0.9990
0.9997 0.9991 0.9976
0.9919 0.9829
0.9972 0.9933
1.0000
0.9999
1.0000
0.6
0.9999
1.0000
3.0
"
3.5
0.9
0.4066
0.7725
4.0
4.5
0.4405
0.6160
0.9945
0.9997 0.9992 0.9980
0.9999 0.9997
0.9993
1.0000 0.9999
0.9998
1.0000
0.9999
1.0000
5.0
0.7622
0.8666
0.9319
0.9682
0.9863
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 10 images
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON