Question $1$: $[20$pt$]$

The manager of the Safeway store $($close to Santa Clara University$)$ is considering improving the

customer service level by reducing customers$$ average waiting time for checkout. Based on the past

year$$s data, they know that customers try to check out every $2$ minutes, on average, and the standard

deviation of the interarrival time is also $2$ minutes. It takes on average $3$ minutes to finish the

checkout process. The standard deviation of the processing times is $3$ minutes. The manager$$s goal is

to make sure the customers$$ average waiting time is less than $0\mathrm{.}5$ minute. At least how many

checkout cashiers should the manager use?