Andy Archer PhD is a training consultant for six midsized ma

Andy Archer, Ph.D., is a training consultant for six mid-sized manufacturing firms. On the average,

each of his six clients calls him for consulting assistance once every 25 days. Andy typically spends an

average of five days at the client\'s firm during each consultation.

Assuming that the time between client calls follows an exponential distribution, determine the

following:

a. the average number of clients Andy has on backlog

b. the average time a client must wait before Andy arrives to it

c. the proportion of the time Andy is busy

Solution

a) average number of clients Andy has on backlog = 6*5 / 25 = 1.2.. [ no. of clients in backlog follows a poisson distribution with mean = 5/25 for 1 client and 6*5/25 for all 6 of them ]

b) average time a client must wait before Andy arrives to it = 1 / [ 5 / 25 ] = 5..days

[ exponential distribution with mean 1 / lambda , lambda = 5 / 25 ]

c) the average no. clients Andy has on backlog is more than 1 right! so, when he has clients on backlog ,
his working days are not less than 25..

so, proportion is 1...all the time Andy is busy!