Problem $2(12$ points$)$

Trucks are required to pass through a weighing station so they can be checked for weight violations. Trucks arrive at the station at the rate of $40$ an hour between $7$:$00$ p$.$m$.$ and $9$:$00$ p$.$m$.$ Currently two inspectors are on duty during those hours, each of whom can inspect $25$ trucks an hour.

a$.$ How many trucks would you expect to see at the weighing station, including those being inspected?

Note: Round your answer to $3$ decimal places.

b$.$ If a truck was just arriving at the station, about how many minutes could the driver expect to be at the station?

Note: Round your answer to $2$ decimal places.

c$.$ What is the probability that both inspectors would be busy at the same time?

Note: Round your answer to $4$ decimal places.