" Don't ask what it means, but ratherhow it is used." - L. Wittgenstein (1889 -1951)

5.3 SIMULATING EXPERIMENTS (Pages 286 -296)

OVERVIEW: Simple devices,such as random number generators, dice, cards, spinners, etc. can beused to "imitate" chance outcomes and to obtain empiricalprobabilities relating to real-life events.

Simulation: Theimitation of chance behavior in an attempt to gain information abouta real-life situation.

On TI-83, randInt( can be used to generaterandom integers.

Steps in creating a simulationmodel:

1. State the problem or describe theexperiment.
2. State the assumptions.
3. Assign digits to represent outcomes.
4. Simulate many repetitions.

Here is a simulation using TI-83:

PREMISE:
Herky Airline planes have 40 seats.
There is a 90% probability that a ticket purchaser will show up for ascheduled flight.
President Herky decides to sell 43 tickets for each sight.
What is the probability of an oversoldsituation?

Brief outline of process:

Generate 43 random digits from the set{0,1,2,3,4,5,6,7,8,9}
Let 9 represent a ticket purchaser who does not show up.
Count the number of 9's in each set of 43 random digits.
Then, 43 - (number of 9's) = S = number of purchasers who show up forflight.
If S > 40, flight is oversold.
Repeat many times, each time recording the result (oversold ornot).

When trials are completed, determine empiricalprobability by calculating the ratio (number of oversoldsituations)/(total number of trials).

This sequence of commands allows for a simulationof the Herky Airline problem on the TI-83.

ClrList L1,L2
1->C
randInt(0,9,43)->L1:sum(L1<9)->L2(C):1+C->C

When you hit ENTER, a random list of digits isstored in L1. The command sum(L1<9) calculates the frequency ofdigits that are less than 9, and stores that in the appropriate cellin L2. Upon pressing ENTER, the first such frequency is stored inL2(1). Then, pressing ENTER completes a second trial, and the resultsfrom the second trial are stored in L2(2).

Simply continue this process to complete as manytrials as you like. When you are done, STAT/EDIT will display theresults of your trials stored in L2.