MetaAfter a five$-$hour shift watching for speeders on Hwy $75,$ Officer Scott Turner returned to his station with

$$600$ in speeding tickets. His supervisor was upset, since he thought that $$600$ was unusually low for such a

long shift. $$Stop spending so much time at the Donut Palace!$$ he says. Scott responded that he was not

wasting time, claiming it was a slow day on the highway.

Fines are determined based on how many miles per hour the driver is over the posted speed limit$.$ The

department policy is to pull over any driver going more that $10$ mph over the posted speed limit$.$ Based on

past observations, the department has estimated the percentage of drivers that speed $($table below$).$ On a

typical day, a police officer will observe on average one car per minute $($inter$-$car times are an exponential

distribution with rate $=1)$ and it takes on average $30$ minutes $($exponential distribution with rate $=1/30)$

to stop a speeder and issue a ticket $($no warnings!$).$

MPH over Speed Limit Fine Percent of Drivers

Less than $10$ $$090\%$

$11-15$ $$1007\%$

$16-20$ $$2002\%$

More than $20$ $$3001\%$

Was Officer Turner telling the truth? Conduct a simulation to estimate the probability of issuing only $$600$

$($or less$)$ in speeding tickets in a five$-$hour $(300$ minute$)$ shift. To do this, count what proportion of simulations

have a total ticket value less than or equal to $$600.$

Note: Occasionally an officer will have to give a ticket in the last $30$ minutes of their shift. In this case, he

will give the ticket, even though it means that he will likely be on duty for more that $300$ minutes.