Customers checking out at Food Tiger arrive in a single$-$line queue served by two cashiers at a rate of $7$ per hour according to a Poisson distribution. Each cashier processes customers at a rate of $9$ per hour according to an exponential distribution.

$($a$)$

If$,$ on average, customers spend $32$ minutes shopping before getting in the checkout line, what is the average time $($in minutes$)$ a customer spends in the store? $($Round your answer to two decimal places.$)$

minutes

$($b$)$

What is the average number of customers waiting for service in the checkout line? $($Round your answer to four decimal places.$)$

customers

$($c$)$

What is the probability that a customer must wait? $($Round your answer to four decimal places.$)$