a) the probability that during a​ 1-minute period zero phone
calls will be​ received is,
P(k=0)=e-1 *(10 /0!)=e-1
=0.3679
Excel function:
P(k=0)=POISSON(0,1,FALSE)=0.3679
b) the probability that during a​ 1-minute period three or more
phone calls will be​ received is,
P(k>=3)=1-e-1 *(
10/0!+11/1!+12/2!)
               Â
=1-0.3679(1+1+0.5)
               Â
=1-0.3679*2.5
                Â
=1-0.9197
                Â
=0.0803
Excel function:
P(k>=3)=1-POISSON(2,1,TRUE)=0.0803
c) maximum number of phone calls that will be received in a​
1-minute period​ 99.99% of the​ time is,
| No. of calls(x) |
POISSION(x,1,TRUE) |
|
|
| 3 |
0.9810 |
| 4 |
0.9963 |
| 5 |
0.9994 |
| 6 |
0.9999 |
| 7 |
1.0000 |
| 8 |
1.0000 |
Hence,maximum number of calls is 6 in a 1
minute period 99.99% of the time.
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