Solution-Â Â To find Poisson
distribution probabilities in Excel, use the function
=POISSON(x;?;0)
x=number of occurrences over a specified interval
?=average number of occurrences over a specified interval =
20
since the probability distribution in excel for an interval of
30 minute duration given below.
|
x   |
p(X=x) |
Round off at six places |
|
0 |
2.06115E-09 |
0 |
|
1 |
4.12231E-08 |
0 |
|
2 |
4.12231E-07 |
0 |
|
3 |
2.7482E-06 |
0.000003 |
|
4 |
1.3741E-05 |
0.000014 |
|
5 |
5.49641E-05 |
0.000055 |
|
6 |
0.000183214 |
0.000183 |
|
7 |
0.000523468 |
0.000523 |
|
8 |
0.001308669 |
0.001309 |
|
9 |
0.002908153 |
0.002908 |
|
10 |
0.005816307 |
0.005816 |
|
11 |
0.010575103 |
0.010575 |
|
12 |
0.017625171 |
0.017625 |
|
13 |
0.027115648 |
0.027116 |
|
14 |
0.03873664 |
0.038737 |
|
15 |
0.051648854 |
0.051649 |
|
16 |
0.064561067 |
0.064561 |
|
17 |
0.075954196 |
0.075954 |
|
18 |
0.084393552 |
0.084394 |
|
19 |
0.088835317 |
0.088835 |
|
20 |
0.088835317 |
0.088835 |
|
21 |
0.084605064 |
0.084605 |
|
22 |
0.076913695 |
0.076914 |
|
23 |
0.066881474 |
0.066881 |
|
24 |
0.055734561 |
0.055735 |
|
25 |
0.044587649 |
0.044588 |
|
26 |
0.034298192 |
0.034298 |
|
27 |
0.025406068 |
0.025406 |
|
28 |
0.018147191 |
0.018147 |
|
29 |
0.012515304 |
0.012515 |
|
30 |
0.008343536 |
0.008344 |
probability that no more then 14 customers will arrive =
P(X<_14)
= probability sum of 0 to 14 of above
table.
= 0.104864
