Problem $3(10$pt$)$

Consider the check$-$out counter at a local grocery store. Customers arrive at the check$-$out counter

every $10$ min on average with a standard deviation of $7$ min. The store has only one cashier who

scans and bags the groceries. It takes the cashier $9$ min on average with a standard deviation of $5$

min to scan and bag the groceries for a customer.

a$.$ What is the utilization of the cashier? $(1$pt$)$

b$.$ What is the average waiting time for a customer in queue? $(3$pt$)$

c$.$ What is the average number of customers waiting in the check$-$out line $($i$.$e$.,$ excluding any

customer being served$)?(1$pt$)$

d$.$ After attending a training program, the cashier can scan and bag groceries for a customer in $6$

min on average with a standard deviation of $3$ min. What is the reduction in average customer

waiting time $($in minutes$)$ because of this training program? $(5$pt$)$