The photo booth at the Apple County fair takes snapshots in exactly 90 seconds. Customers arrive...

The photo booth at the Apple County fair takes snapshots in exactly 90 seconds. Customers arrive at the machine according to a Poisson distribution at the mean rate of 25 per hour. Using this information, determine the following:

a.	the average number of customers waiting to use the photo machine
b.	the average time a customer spends in the system
c.	the probability an arriving customer must wait for service.

Expert Solution

Answer:

Given,

Arrival rate = 25 per hour

Service rate = 3600/90 = 40 per hour

a)

Average number of customers waiting to use the photo machine Lq = ^2/(-)

substitute values

= 25^2 / (40(40 - 25))

= 1.042

b)

average time a customer spends in the system W = 1/(-)

= 1 /(40-25)

= 1/15

= 0.0667 *60

= 4 min

c)

probability an arriving customer must wait for service = /

= 25/40

= 0.625

= 62.5%

orchestra answered 3 years ago

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