A small diner has one employee and a counter with seating for $8$ customers. The diner does not

package food for takeout. Customers arrive at the diner at the rate of $20$ per hour $($Poisson

distributed$).$ Service times are exponentially distributed and average $24$ per hour. Customers that

arrive when all seats are taken do not enter the diner. What is the average number of customers in

the diner?

$2\mathrm{.}0432$

$5\mathrm{.}4837$

$2\mathrm{.}8352$

$3\mathrm{.}7536$