Question 1

The management at BuyRite grocery stores wishes to estimate the amount of time that customers are spending, on average, in its stores and in a checkout line. The most obvious approach for determining this information is to simply record when a customer enters and exits the store. However, it is difficult to track the entering and exiting times of specific customers. We will look at the problem using an alternative approach. Over the past two weeks, the following data have been collected at BuyRite’s newest store during busy hours (this BuyRite is rather large and typically has 7 open checkout lines). For simplicity, let us assume that the overall capacity at checkout lines is higher than the arrival rate of customers into the store.

Average rate of customers entering store = 305 customers/hour
Average number of customers in store = 146 customers
Percentage of customers who do not make a purchase = 5%
Average number of customers in the checkout lines = 24 customers

As their consultant, you have been asked by BuyRite’s management to address the following questions:

(a) How much time on average does a customer spend in the store?

(b) How much time on average does a customer spend waiting?

Question 2

The following two sub questions (a) and (b) are independent from each other.

(a) The student recreation center at a large Midwestern university has a computerized stationary bicycle. During peak periods, students arrive to use that bicycle at the average rate of three per hour, Poisson distributed. Each person rides for an average of fifteen minutes, but riding times are exponentially distributed. Please answer the following questions:

(1) How many students would you expect to see waiting for the bicycle, assuming all who arrive wait?

(2) What percentage of time is the bicycle being used?

(3) What