as measured by average arrival rates $($below$).$

Morning $(8$:$30-11$:$30)$: $,$ arrival $1=38$ per hour.

Lunch $(11$:$30-1$:$30)$ : $,$ arrival $2=27$ per hour.

Afternoon $(1$:$30-4$:$00)$:$,$ arrival $3=47$ per hour.

Regardless of the time of day, the average time it takes for a teller to serve customers is $3\mathrm{.}5$ minutes.

Because of competition with other banks in the area, management has developed an internal goal to keep the average customer wait before service to be less than $5$ minutes. With that in mind, answer the following:

a$.$ During the morning period, what is the minimum number of tellers that the bank needs to hire to achieve the $5-$minute service goal mentioned above?

b$.$ During lunch, what is the minimum number of tellers that the bank needs to hire to achieve the $5$ minute service goal mentioned above?

c$.$ In the afternoon, what is the minimum number of tellers that the bank needs to hire to achieve the $5$ minute service goal mentioned above?

d$.$ In the evening, based on the amount of tellers needed to meet the goal, what is the average number of customers waiting before they get served?

$,$ and the time waiting before being served?

minutes