# Math 2311

MATH 2311 Section 6.3 Simulating Experiments Simulation is the imitation of a chance behavior based on a model that reflects an experiment. This is done when running an actual experiment is too dangerous, too costly, or too time-consuming, or if there are other ethical concerns involved with running an actual experiment. These will involve using the random digit table (appendix of the textbook). You must assign the digits based on the percentages that are given in the question.

(If you need to represent 20% you should be assigning 2 out of 10 digits. These can be 0, 1 or 8, 9) One run of the experiment, means that you are looking at one block of digits of numbers from the table. 8% of customers are no-shows. Therefore, 92% of customers showed up for their flight. One run would mean 17 numbers (to represent the 17 tickets sold) 2 digit numbers (our percents are not multiples of 10) 00 to 91 representing customers that shows up. (92 out of 100) 92 to 99 representing customers that did not show up (8 out of 100) 98 36 02 65 34 47 38 49 46 12 88 66 61 41 70 10 84

N S S S S S S S S S S S S S S S S Random Number Table: Digits: 0 91: Customer showed up; Digits 92-99: Customer did not show up. Pick a line to begin the experiment. See how many customers showed up out of 17 tickets sold. Did the company make money or not? Results: of 17 tickets sold, only 1 did not show up. Recommendation: sell 16 tickets instead of 17 a. Heads: 0, 1, 2, 3, 4; Tails: 5, 6, 7, 8, 9 (Each of these categories is 5 out of 10 options, so 50%)

b. One repetition of this experiment would be a twenty-number block. First Run: TTHTH HTTHH HTHTH THTHHLongest run of heads: 3 in a row Second Run: TTTTT HHHTH HHTHT HTTTT Longest run of heads: 3 in a row (occurs twice) Third Run: TTTTT TTTTH TTTHT HHHTH Longest run of heads: 3 in a row Popper 20: 20% (2 of 10) do not have classes; 80% (8 of 10) do have class

It has been determined that 20% of students do not have scheduled classes one day of out the week. A university is considering to sell 25 parking permits for a parking lot with only 20 spaces to account for this. This practice will go into effect if a simulated experiment has less than 2 students unable to park their car. 1. How would you assign random digits for this situation? a. 0, 1, 2: students with no scheduled classes; 3 9: students with class b. 0 7: students with no classes; 8, 9: students with class. c. 0 7: students with classes; 8, 9: students without classes.

d. 0, 1: student with classes; 2 9: students without classes. Popper 20, continued: (Using 0 7 to represent students with scheduled classes, and 8 9 representing students without scheduled classes): NNCCC CCCCC CCCNC

NCCCC NNCCC Total: 6 No class, 19 Class 2. Simulate the experiment using the first 25 digits from this line of the random digit table: a. Out of 25 parking passes sold, only 19 students had class. b. Out of 25 parking passes sold, only 6 had class. c. Out of 25 parking passes sold, 24 students had class. d. Out of 25 parking passes sold, 22 students had class.

3. Should the university go ahead with this practice? e. Yes b. No 4. If another line of the Random Digit Table were used, would these results be the same? a. Yes b. No

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