Problem $18-6($Algo$)$

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 $24$ 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 $15$ trucks an hour. Use Table $18\mathrm{.}4.$

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.

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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.

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minute

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

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

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d$.$ How many minutes, on average, would a truck that is not immediately inspected have to wait?

Note: Round your answer to the nearest whole number. minute