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?

Answer 1

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,

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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