5.2 Using Simulation to Estimate Probabilities

HW: E’s 15, 17, 19, 21

Steps in a Simulation using Random Digits

1. Assumptions. State the assumption you are making about how the real-life situation works. Include any doubts you might have about the validity of your assumptions.

Steps in a Simulation using Random Digits

2. Model. Describe how you will use random digits to conduct one run of a simulation of the situation.– Make a table that shows how you will assign a

digit or group of digits to represent each possible outcome

– Explain how you will use the digits to model the real-life situation. Tell what makes a single run and what summary statistic you will record

Steps in a Simulation using Random Digits

3. Repetition. Run the simulation a large number of times, recording the results in a frequency table. You can stop when the distribution doesn’t change to any significant degree when new results are include

Steps in a Simulation using Random Digits

4. Conclusion. Write a conclusion in the context of the situation. **Be sure to say you have estimated probability.**

Pg 302: Hourly Workers at Westvaco

The ages of ten hourly workers involved in layoffs were 25, 33, 35, 48, 55, 55, 55, 56, & 64. Three workers laid off were 55, 55, 64 for an average of 58. Use a simulation with random digits to estimate the probability that three workers selected at random for layoff would have an average of 58 or more.

Pg 302: Hourly Workers at Westvaco

• Assumptions• Model• Repetition• Conclusion

Pg 303: Hand Washing

Test the probability that all four people using a public restroom washed their hands based on a 67% wash rate.1. Assumptions2. Model3. Repetition4. Conclusion

Pg 309 D11

For the example Hand Washing, describe another way the random digits could have been assigned using pairs of random digits. Describe a way that uses triples of random digits.Any assignment with 67 pairs of digits to washer could work. Three digits could be 001-670.

PG 308 Blends of Coffee

Coffee house rotates amount six different blends of coffee. Supposed you go into the coffee house on three randomly selected days. Estimate the probability that the house will be offering a different blend each of the three days.1. Assumption 2. Model.3. Repetition 4. Conclusion

Pg 309 D12

Describe how to use a die to simulate the situation in the coffee house example.Assign a roll of 1 to the first blend, a roll of 2 to the second blend, etc. Roll three times and record whether all rolls are different.

Pg 310 P10

How would you use a table of random digits to conduct one run of a simulation of each situation?a) There are eight workers, ages 27, 29, 31, 34,

34, 35, 42, 47. Three are to be chosen for layoff.

b) There are 11 workers ages 27, 29, 31, 34, 34, 35, 42, 42, 42, 46, 47. Four are to be chosen.

Pg 310 P10

a) Assign each worker to a random digit. Start at a random place at in the random table and look at the next three digits. Those digits will represent workers selected to be laid off. If a 9 or 0 appears, ignore it. Also, ignore duplicates since a person can’t be laid off twice.

b) Since there are more than ten workers, assign pairs of digits to a set of 10 numbers. Skip duplicates.

Pg 310 P11

a) Assumptions: Assuming probability each teaspoon has 0.80 of disappearing within five months and the disappearances of individual spoons are independent.

b) Model: Disappeared 1-8 | Did not 9, 0c) Repetition: Starting a row 34 of Table D. First ten

digits are 58 80 80 83 91 -- add 10 more runs to table

d) Conclusion: 517 out of 5000 runs resulted in all ten spoons disappearing.

Pg 310 P12

• Assumption: you have a random sample w/o replacement of size 9 from a population of 101 catastrophic accidents of which 55 resulting from cheerleading.

• Model: Assign triple digit numbers to each accident and ignore repeats. (faster to assign 9 triple digits) 011-019 = 1 Complete 10 runs

• Repetition: Divide digits into triples and ignore doubles

• Conclusion: 722/1000 runs

Pg 311 P13

• Assumption: Assume a probability of a given team winning a particular game is 50% and results are independent.

• Model: Assign digits 1-5 to team A winning and 6-9, 0 to team B winning. Allow repeats. Continue until one team gets 4 wins.

• Repetition: Separate each row by a completed series

• Conclusion: 1537/5000 went full seven games