Question

In: Statistics and Probability

People arrive to a hotel at a rate of 20 on average with each half hour....

People arrive to a hotel at a rate of 20 on average with each half hour. Make a probability distribution in excel for an interval of 30 minute duration. What’s the probability that no more then 14 customers will arrive?

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Expert Solution

Solution-  To find Poisson distribution probabilities in Excel, use the function =POISSON(x;λ;0)

x=number of occurrences over a specified interval

λ=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


orchestra answered 2 years ago
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