The manager of a library is planning to use simulation to analyze the operations of the library.

One of the elements of the models requires simulating how long an employee spends processing late

fees. The manager estimates that probability distribution that describes the time spent processing

late fees $($in minutes$)$ has the cumulative distribution function $($CDF$)$ shown in the graph below.

$($a$)$ Generate three pseudo$-$random numbers using the linear congruential generator $($LCG$)$ method

with parameters a $=43,$ c $=3,$ m $=16,$ and Z$0=5.$ Make sure that you show all of your

work and explain how you arrived at your answers.

$($b$)$ Use the inverse transformation method to generate a random variate drawn from the dis$-$

tribution described above to simulate the time needed to process the late fees for each of

pseudo$-$random numbers generated in $($a$).$ Be sure to show all of your work and explain how

you arrived at your answers.

$3$