$(50)$ The time between arrivals of cars at the Petrol Service Station is defined by the following

probability distribution:

Time Between Arrivals $($min$.)$ Probability

$10\mathrm{.}15$

$20\mathrm{.}30$

$30\mathrm{.}40$

$40\mathrm{.}15$

$1\mathrm{.}00$

a$.$ Simulate the arrival of cars at the service station for $20$ arrivals and compute the average time

between arrivals.

b$.$ Simulate the arrival of cars at the service station for $1$ hour, using a different stream of random

numbers from those used in $($a$)$ and compute the average time between arrivals.

c$.$ Compare and comment on the results obtained in $($a$)$ and $($b$).$