Submit a report, as well as your Python code, reflecting your work for the following steps.

$($a$)$ State all the entities, resources, and queues of the system.

$($b$)$ Find a suitable Arena expression random distribution for the total eating time for a

group of size $k,$ i$.$e$.,$ the time between the start of the meal by the group and the end

of eating by the latest person in the group. $[$Hint $1$: If $xUnif(a,b),$ you can express

$x=a+(b-a)Y$ where $YUnif(0,1).$ Hint $2$: What is the distribution of the maximum

of $k$ i$.$i$.$d$.$ random variables with a uniform distribution Unif$(0,1)?]$

$($c$)$ On Python, do the following using the recorded values Task$3\_$MainSideSoup$\_$times.csv:

i$.$ Generate a histogram of the recorded values in the file.

ii$.$ Fit a normal distribution to the recorded values in the file using maximum likelihood

estimation. State the parameters you calculated.

iii. Perform a chi$-$square test with significance level $=0\mathrm{.}05$ for

$H_0$ : The process time has a normal distribution. vs $H_1$ : Not $H_0.$