A toll-free phone number is available from 9 a.m. to 9 p.m. for your customers t

Question

A toll-free phone number is available from 9 a.m. to 9 p.m. for your customers to register complaints about a product purchased from your company. Past history indicates that an average of 1.0 calls are received per minute. Complete parts (a)through (c).

A.    what is the probability that during a 1 min period zero phone calls will be received?

B.    what is the probability that during a 1 min period three or more phone calls will be received?

C.    what is the maximum number of phone calls that will be received in a 1 min period 99.99% of the time?

Explanation / Answer

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!)

                 =1-0.3679(1+1+0.5)

                 =1-0.3679*2.5

                  =1-0.9197

                  =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,

Hence,maximum number of calls is 6 in a 1 minute period 99.99% of the time.

Please upvote my answer if you like..

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

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