Question

Suppose that the average number of new clients that a sales representative signs in a month is 22 and that the distribution of this random variable is Poisson. What is the probability that any given sales representative will sign fewer than 15 new clients in a month?

Answer 1

Ans:

Poisson distribution with rate=22 per month

P(x=k)=e^-22*(22^k/k!)

P(x<15)=P(x<=14)

=POISSON(14,22,TRUE)=0.0477

or use below table:

x	P(x)
0	0.0000
1	0.0000
2	0.0000
3	0.0000
4	0.0000
5	0.0000
6	0.0000
7	0.0001
8	0.0004
9	0.0009
10	0.0020
11	0.0041
12	0.0075
13	0.0127
14	0.0199
Total	0.0477