1. Chapter 11 Understanding Randomness

2. What does it mean to be random? An outcome is random if we know the possible values it can have, but not which value it will take.

3. Random numbers are hard to generate, but we have a few ways to make a good attempt at randomness: Appendix G in your textbook Random number generator on TI calculators Random number generators online

4. Generating random numbers on TI-84 MATH  PRB  5: randInt Give the range of values you want to use. Example: randInt(1,20) will generate a number between 1 and 20. To generate a list of random numbers, add a third command. Ex: randInt(1,20,5) will generate 5 numbers between 1 and 20.

5. Example of a Simulation: A cereal company is giving away prizes in cereal boxes. If 50% of cereals give a blue prize, 30% of bottles give a red prize, and 20% of bottles give a green prize, how might we use a random number generator to simulate how many boxes we’d have to buy before having one of each color of prize?

6. Assign blue (50%) the digits 0, 1, 2, 3, 4 Assign red (30%) the digits 5, 6, 7 Assign green (20%) the digits 8, 9 Generate random numbers to see how many boxes would be purchased This is one trial. Run several trials for more accuracy. The more trials the better. Look at summary statistics to make your conclusion (draw a boxplot, look at median and IQR)

7. Numberphile Video about Randomness

8. Practice A manufacturer of batteries knows that 10% of its batteries come off the production line defective and the remaining 90% of batteries come off the line in working condition. Conduct a simulation to estimate how many batteries the company needs to pull off the production line in order to be sure of ending up with 10 working batteries. Use the random number tables to conduct 3 trials. 10242 50692 18977 28370 82669 83236 77479 90618 43707 81183 48554 60809 39996 81915 25404 33366 92082 04822 06765 67041 20479 54612 13411 36837 69983 53082 43589

9. Assign 0 to bad batteries and 1-9 to good batteries: 10242 50692 18977 28370 82669 83236 77479 90618 43707 +X+++ +X+++ ++| end of Trial 1  12 needed to get 10 working batteries 81183 48554 60809 39996 81915 25404 33366 92082 04822 +++++ +++++| end of Trial 2  10 needed to get 10 working batteries 06765 67041 20479 54612 13411 36837 69983 53082 43589 X++++ ++X++ +X+| end of Trial 3  13 needed to get 10 working batteries Based on these 3 trials, the company needs to pull at least 13 batteries to be sure of obtaining 10 working batteries.

10. Based on experience, a float decorator found that 10% of the bundles of roses delivered will not open in time for the parade, 20% of them will have bugs on them and be unusable, 60% will be just right, and the rest will have bloomed too soon and will discolor before the parade. Conduct a simulation to estimate how many roses the float decorator will need to purchase to have 15 good bundles. Show 4 trials using the random number tables. 37542 04805 64894 74296 24805 24037 20636 10402 00822 08422 68953 19645 09303 23209 02560 15953 34764 35080 99019 02529 09376 70715 38311 31165 88676 74397 04436 12807 99970 80157 36147 64032 36653 98951 16877 12171

11. Not Open = 0; Bugs = 1, 2; Good Roses = 3, 4, 5, 6, 7, 8; Bloomed Early = 9 37542 04805 64894 74296 24805 24037 20636 10402 00822 ++++X X++X+ +++X+ ++XX+ X+ | end Trial 1  22 bundles needed 08422 68953 19645 09303 23209 02560 15953 34764 35080 X++XX ++X++ XX+++ XX+X+ X+XXX XX++X X+ | end Trial 2  32 bundles 99019 02529 09376 70715 38311 31165 88676 74397 04436 XXXXX XX+XX XX+++ +X+X+ +++XX +XX++ ++ | end Trial 3  32 bundles 12807 99970 80157 36147 64032 36653 98951 16877 12171 XX+X+ XXX+X +XX++ ++X++ ++X+X ++ | end Trial 4  27 bundles The float director needs to purchase at least 32 bundles of roses to be sure of obtaining 15 bundles of beautiful roses.

12. Today’s Assignment:  ESP Activity  READ CHAPTER 11!!! (It’s only about 5 pages)  HW: p.265 #5-7, 19

13. Your friend claims he has ESP. Being skeptical, you decide to test his claim. Here’s the plan. You get 10 people to sign their names on identical cards and seal them in envelopes. Using his alleged powers, he will distribute the envelopes to the 10 people. It’s unlikely that he’ll return each envelope to its owner. Chances are he’ll match some and miss others. Use a simulation to decide how many matches an ordinary person might make by chance. Do a simulation with at least 20 trials. You may use a calculator or a random number table. Include an explanation of your procedure and the results of the trials. How many matches would your friend need to make to convince you he has ESP? ESP Activity