Question

12) [30 pts] Poisson statistics assume that the number of pieces of mail delivered to Dr. Scarpulla's home each day follows Poisson statistics. Last year, his home tallied 1,800 pieces of mail in 365 days. Make an excel table predicting the number of days that 0, 1, 2...10 pieces of mail were delivered last year. 1) calculate the Poisson distribution for integer values 0 through 10 for the average number of pieces of mail per day. 2) make sure if you sum the pieces of mail delivered number of days that should happen, you get the total number of pieces of mail for the year. C) also make sure that the predicted number of days in the 11 categories of pieces of mail delivered sums to 365.

Answer 1

average number of mail in a day=1800/365=4.93 ( two decimal place approximation)

now here we use poisson distribution with parameter $\lambda$ =4.93 and for poisson

P(X=x)=exp(- $\lambda$ ) $\lambda$ ^{^x}/x!

(1)

x	P(X=x)
0	0.0072
1	0.0356
2	0.0877
3	0.1442
4	0.1778
5	0.1754
6	0.1442
7	0.1016
8	0.0626
9	0.0343
10	0.0169
>11	0.0125
total	1.0000

(2) and (C)

number of mail=n*p(X=x)=1800*P(X=x)

x	P(X=x)	number of mail
0	0.0072	13
1	0.0356	64
2	0.0877	158
3	0.1442	260
4	0.1778	320
5	0.1754	316
6	0.1442	259
7	0.1016	183
8	0.0626	113
9	0.0343	62
10	0.0169	30
>11	0.0125	22
total	1.0000	1800