two random variables you need to considet the thte at which calls arrive and the time it takes an operator to process a pledge.

Pledge culls are expected to arrive according to the following distribution

$\backslash$table$[[\backslash$table$[[$Inter$-$arrival time: Time$],[$between$]]],[$calls arriving at phone bank$],[($minutes$)]]$ prohbility

And the probability distribution below reflect the anounlofine whone operior needs to gather the information needed toprocess shleg:

$\backslash$table$[[\backslash$table$[[$Time required for phone$],[$operator to process the$],[$phone call$],[($minutes$)]],$Probability$],[1,20],[2,15],[3,25],[4,27],[5,13]]$

Use the following pairs of random numbers to simulate the artyalind processing of six phone calls $($by a single operator$).$ Let the first number in each bair determine als calls inter$-$arrival time and the second number the time to process a call. Estinute the rverygecter waiting time.

$(85,31)(55,76)(74,54)(22,55)(60\mathrm{.}72)(12\mathrm{.}90)$

You should assume that the first call arrives at fime $($i$.$e$.$ the $85$ in the first pair of random numbers is not needed$).$

Answer questions $1-6$ by referencing the above in formation.

At what time will the third phone call arrive?

What is the time required to process the fourh phone call?

When does the operator begin processing the fourth call?

How long is the fifth caller on hold?

How long is the sixth caller on hold?

For the six callers simulated above, what is the average time on hold $($in minutes$)?$

The manager of a small post office is concerned that the growing township is overloading the one$-$window service being offered. Sample data are collected on $100$ individuals who arrive for service:

$\backslash$table$[[\backslash$table$[[$Time between$],[$Arrivals$],[($minutes$)]],$Frequency$],[1,8],[2,35],[3,34],[4,17],[5,6]]$

$\backslash$table$[[\backslash$table$[[$Service Time$],[($minutes$)]],$Erequency$],[1\mathrm{.}0,12],[1\mathrm{.}5,21],[2\mathrm{.}0,36],[2\mathrm{.}5,19],[3\mathrm{.}0,7],[3\mathrm{.}5,5]]$

Using the following random number sequence, simulate six arrivals, assume the first arrival is