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.
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.
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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The number of customers arriving per hour at a certain automobile service facility is assumed to follow a Poisson distribution with
(a) Compute the
(b) What is the mean number of arrivals during a 2-hour period.
Transcribed Image Text:P
5.5
6.0
6.5
0.0015
9.5
0.0001
0
0.0041
7.0
0.0009
0.0073
0.0025
0.0174
1
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
"
7.5
8.0
8.5
9.0
0.0006 0.0003 0.0002 0.0001
0.0030
0.0047
0.0012
0.0019
0.0008
0.0138 0.0093 0.0062 0.0042
0.1118 0.0818 0.0591 0.0424 0.0301 0.0212 0.0149
0.2237 0.1730 0.1321 0.0996
0.0744 0.0550
0.0403
0.3690 0.3007 0.2414 0.1912 0.1496 0.1157 0.0885
0.3134 0.2562 0.2068 0.1649
0.4530 0.3856 0.3239 0.2687
0.5925 0.5231 0.4557 0.3918
0.7166 0.6530
0.5874 0.5218
0.8159 0.7634 0.7060
0.6453
0.8881 0.8487 0.8030
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
0.9208
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
0.9862 0.9780 0.9665
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
1.0000 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
18
0.9999 0.9998 0.9996 0.9991
1.0000
19
20
21
22
23
24
P
5.5
Poisson Probability Sums Σ p(x;μ)
r=0
6.0
6.5
7.0
7.5
"
8.0
0.9999 0.9998 0.9996
1.0000 0.9999
1.0000
0.9999
0.9999
1.0000
9.5
8.5
9.0
Q=
10
r
0
1
2
3
4
5
6
P
6 C
0
1
3
4
5
NDODHEBH59
7
8
10
11
12
"
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
0.3679 0.2231 0.1353
0.0821
0.0498 0.0302 0.0183 0.0111 0.0067
0.7358 0.5578 0.4060 0.2873 0.1991 0.1359 0.0916 0.0611 0.0404
0.919
088
767 0.5438 0.4232 0.3208 0.2381 0.1736 0.15
0.9810 0.9344 0.8571 0.7576 0.6472 0.5366 0.4335 0.3423 0.2650
0.9963 0.9814 0.9473 0.8912 0.8153 0.7254 0.6288 0.5321 0.4405
0.9994
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
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
13
14
15
16
P
"
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9048 0.8187 0.7408 0.6703 0.6065 0.5488 0.4966 0.4493
0.9953 0.9825 0.9631 0.9384 0.9098 0.8781 0.8442 0.8088
0.9998 0.9989 0.9964 0.9921
0.9769
0.9856
0.9526
0.9659
1.0000 0.9999
0.9992 0.9982
0.9942
0.9997
0.9909
0.9966
1.0000 1.0000 0.9999 0.9998 0.9996 0.9992 0.9986
1.0000 1.0000
0.1
Poisson Probability Sums Σ. p(x;μ)
T=0
1.0
0.2
0.3
1.5
0.4
2.0
0.5
μl
2.5
0.9977
1.0000 0.9999 0.9998 0.9997
1.0000 1.0000 1.0000
0.7
0.8
0.9
0.6
3.0
"
0.9999 0.9997 0.9991 0.9976
1.0000 0.9999 0.9997 0.9992
1.0000 0.9999
0.9997
1.0000 0.9999
1.0000
3.5
0.9
0.4066
0.7725
0.9371
0.9865
4.0
4.5
0.9945
0.9980
0.9993
0.9998
0.9999
1.0000
5.0
Transcribed Image Text:T
10.0
11.0
12.0
0 0.0000 0.0000 0.0000
1
2
3
0.0103
4
0.0293
0.0151
5 0.0671 0.0375
11
12
13
14
15
26
27
28
29
30
31
32
0.0259 0.0142
0.0076
6 0.1301 0.0786 0.0458
0.2202 0.1432 0.0895
0.3328 0.2320 0.1550
7
0.0540
0.0316
0.0180
0.0998
0.0621 0.0374
0.0699
8
9 0.4579
0.3405 0.2424 0.1658 0.1094
0.5830 0.4599 0.3472 0.2517 0.1757
0.1185
10
33
34
35
0.6968 0.5793
0.4616 0.3532 0.2600
0.7916 0.6887 0.5760 0.4631
0.3585
0.5704
0.9513
0.8645 0.7813 0.6815 0.5730 0.4644
0.9165 0.8540 0.7720 0.6751
0.9074 0.8444 0.7636 0.6694
16 0.9730
0.9441 0.8987 0.8355 0.7559
0.6641
17 0.9857 0.9678 0.9370
0.8905 0.8272 0.7489
18 0.9928 0.9823 0.9626 0.9302 0.8826 0.8195
19 0.9965 0.9907 0.9787 0.9573 0.9235 0.8752
20
0.9984
0.9953 0.9884 0.9750
0.9521
21 0.9993 0.9977 0.9939
22 0.9997 0.9990 0.9970
23 0.9999 0.9995 0.9985 0.9960
24 1.0000
0.9998 0.9993 0.9980
25
0.9999 0.9997 0.9990
0.9170
1.0000
36
37
Poisson Probability Sums p(x;μ)
T
10.0
0.0076
0.0203
11.0
13.0
0.0005 0.0002 0.0001 0.0000 0.0000
0.0028 0.0012 0.0005 0.0002 0.0001 0.0000 0.0000
0.0049 0.0023 0.0011 0.0005 0.0002 0.0001
0.0037 0.0018 0.0009
0.0028
0.0107 0.0055
x=0
12.0
f
14.0
0.9999 0.9995
0.9999 0.9998
1.0000 0.9999
1.0000
15.0
13.0
0.9859 0.9712
0.9469
0.9924 0.9833 0.9673
0.9907 0.9805
0.9950 0.9888
0.9974 0.9938
"
14.0
0.9987 0.9967
0.9994
0.9983
0.9997 0.9991
0.9999 0.9996
0.9999 0.9998
1.0000
16.0
0.9999
1.0000
15.0
17.0
0.0004 0.0002
0.0014 0.0007
0.1848
0.1270
0.0847
0.0549
0.2676 0.1931 0.1350 0.0917
0.3632 0.2745 0.2009
0.1426
0.4657
0.2808
0.3675
0.5681 0.4667
0.3715
0.0000 0.0000
0.0001
0.0003
0.0040 0.0021
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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