The number of customers arriving per hour at a certain automobile service facility is assumed to follow a Poisson distribution with mean λ = 7. ​(a) Compute the probability that more than 12 customers will arrive in a 2-hour period. ​(b) What is the mean number of arrivals during a 2-hour period.

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.CR: Chapter Review
Problem 37E: Find the positive geometric mean between 4 and 64.
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The number of customers arriving per hour at a certain automobile service facility is assumed to follow a Poisson distribution with mean λ = 7.

​(a) Compute the probability that more than 12 customers will arrive in a 2-hour period.

​(b) What is the mean number of arrivals during a 2-hour period.

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0.0266
0.0113
2 0.0884 0.0620 0.0430 0.0296 0.0203
3 0.2017 0.1512
4 0.3575 0.2851
5 0.5289 0.4457
6 0.6860 0.6063
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0.2237 0.1730 0.1321 0.0996
0.0744 0.0550
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0.3134 0.2562 0.2068 0.1649
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0.5925 0.5231 0.4557 0.3918
0.7166 0.6530
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0.5265 0.4497 0.3782
7 0.8095 0.7440 0.6728 0.5987 0.5246
8 0.8944 0.8472 0.7916 0.7291 0.6620
9 0.9462 0.9161 0.8774 0.8305 0.7764
10 0.9747 0.9574 0.9332 0.9015 0.8622
0.9467
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11 0.9890 0.9799 0.9661
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
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16 0.9999 0.9998 0.9996 0.9990 0.9980 0.9963 0.9934 0.9889 0.9823
17 1.0000 0.9999 0.9998 0.9996 0.9992 0.9984 0.9970 0.9947 0.9911
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18
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19
20
21
22
23
24
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Poisson Probability Sums Σ p(x;μ)
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0.9955 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
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15
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Poisson Probability Sums Σ. p(x;μ)
T=0
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0.9999
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T
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12.0
0 0.0000 0.0000 0.0000
1
2
3
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4
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5 0.0671 0.0375
11
12
13
14
15
26
27
28
29
30
31
32
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0.0076
6 0.1301 0.0786 0.0458
0.2202 0.1432 0.0895
0.3328 0.2320 0.1550
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0.5830 0.4599 0.3472 0.2517 0.1757
0.1185
10
33
34
35
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0.4616 0.3532 0.2600
0.7916 0.6887 0.5760 0.4631
0.3585
0.5704
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0.8645 0.7813 0.6815 0.5730 0.4644
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19 0.9965 0.9907 0.9787 0.9573 0.9235 0.8752
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24 1.0000
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36
37
Poisson Probability Sums p(x;μ)
T
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0.0005 0.0002 0.0001 0.0000 0.0000
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0.9469
0.9924 0.9833 0.9673
0.9907 0.9805
0.9950 0.9888
0.9974 0.9938
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0.9994
0.9983
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1.0000
15.0
17.0
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0.0847
0.0549
0.2676 0.1931 0.1350 0.0917
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0.1426
0.4657
0.2808
0.3675
0.5681 0.4667
0.3715
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0.0001
0.0003
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0.0100 0.0054
0.0220 0.0126 0.0071
0.0433
0.0154
0.0774
0.0304
0.0261
0.0491
0.5660 0.4677
0.6593 0.5640
0.9925
0.9959
0.7423 0.6550
0.8122 0.7363
0.8682 0.8055
0.9108
0.9418
0.9633
0.9777
0.9869 0.9748
16.0
18.0
0.9848
0.9912
0.9978
0.9950
0.9989 0.9973
0.9994
0.0010
0.0029
0.9997
0.9993
0.9999 0.9996
0.9999
0.9998
1.0000
0.9999
1.0000
0.8615
0.7991
0.9047
0.8551
0.9367
0.8989
0.9594 0.9317
0.9554
17.0
0.2081
0.2867
0.3751
0.4686
0.5622
0.6509
0.7307
0.9897
0.9941
0.9986 0.9967
0.9718
0.9827
0.9982
0.9990
0.9995
0.9998
0.9999
0.9999
1.0000
18.0
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ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning