roblem D.1 Hw Score:0%, 0of20 Customers arrive at Rich Dunn\'s Styling Shop at a

Question

roblem D.1 Hw Score:0%, 0of20 Customers arrive at Rich Dunn's Styling Shop at a rate of 3 per hour, distributed in a Poisson fashion. Service times follow a negative exponential distibution Question Hep and Rich can perform an average of 6 haircuts per hour a) The average number of customers waiting for haircuts 50 customers (fround your response to two decimal places b) The avérage number of customers in the shop 1 customers (round your respone to t deplc c) The average time a customer waits until it is his or her turn- minutes (or yourmposetomode· b) The avérage number of customers in he 1 Enter your answer in the answer box and then click Check Answer remaining

Explanation / Answer

We have following information

Arrival rate ? = 3 customers per hour

Service rate µ = 6 customer per hour

a. Find the average number of customers waiting for haircuts

The average number of customers waiting for haircuts = ?^2 /µ * (µ - ?)

= 3^2 / 6 * (6 -3) = 9/ 6 * 3 = 9 /18 = ½ or 0.50 customers

b. Find the average number of customers in the shop.

The average number of customers in the shop = ? / (µ - ?) = 3 / (6-3) = 3/3 = 1 customer

c. Find the average time a customer waits until it is his or her turn

First calculate the average time a customer spends in the shop W = 1 / (µ -?)

= 1 / (6 -3) = 1/3 = 0.333 hours = 20 minutes

Now the average time a customer waits until it is his or her turn Wq = W – 1/µ

= 0.33 – 1/6 = 0.163 hours = 10 minutes

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