Answer to Question #11897 in Statistics and Probability for weiyi

Question

kp cafeteria coffee is very popular. on average it sold 10 cups of coffee per hour. find the probability that exactly 12cups of coffee were sold in 2 hours.

Answer 1

Using Poisson's distribution we will obtain P(0), P(1), ..., P(12). Than Probability we are interested in is calculated as follows P=summ[i=0,12]P(i)P(12-i).

i___P(i)__________P(12-i)_______P(i)P(12-i)
0___0,004540%___9,478033%____0,00043%
1___0,045400%___11,373640%___0,00516%
2___0,227000%___12,511004%___0,02840%
3___0,756665%___12,511004%___0,09467%
4___1,891664%___11,259903%___0,21300%
5___3,783327%___9,007923%____0,34080%
6___6,305546%___6,305546%____0,39760%
7___9,007923%___3,783327%____0,34080%
8___11,259903%__1,891664%____0,21300%
9___12,511004%__0,756665%____0,09467%
10__12,511004%__0,227000%____0,02840%
11__11,373640%__0,045400%____0,00516%
12__9,478033%___0,004540%____0,00043%

And the answer, according to the table(summ of the last column) P=1.76252%