Problem $1$

The Travelers Insurance Company processes $7,526$ claims per year. The average processing time is $2\mathrm{.}4$

weeks. Assuming $50$ weeks in a year, what is the average number of claims $"$in process"?

Problem $2$

A recent analysis at a Staples store by the store manager indicates that, during operating hours, there are

$30$ customers arriving every hour, with a standard deviation of inter$-$arrival times of $3\mathrm{.}1$ minutes. This

arrival pattern is consistent throughout the day. The checkout is currently operated by one employee, who

needs on average $1\mathrm{.}54$ minutes to check out a customer. The standard deviation of this checkout time is

$2\mathrm{.}63$ minutes, primarily because of customers buying different numbers of items.

a$)$ If you assume that every customer buys at least one item $($e$.$ has to go to check out$),$

what is the average time a customer has to wait in line before being served by the

checkout employee?

b$)$ What is the total time a customer spends in line and at the checkout counter being served?

c$)$ What is the average number of customers who are in the system $($i$.$e$.,$ both waiting and

being served$)?$

d$)$ The manager decides that the waiting time is way too long and hires two more checkout

clerks, for a total of three. What is the waiting time $($in the line, before being served$)$ in

this new situation?