1. The document discusses simulations involving coin flips, basketball free throws, and randomly selecting students. It prompts the reader to identify the component, trial, response variable, and statistic for different simulation scenarios. 2. Examples of simulations include flipping a coin 100 times to determine if it is biased, shooting free throws until a miss to measure success rate, and randomly selecting 3 students from a class. 3. The reader is asked to consider how the simulations would change based on the probability of success, number of trials, and structure of dependent vs independent events.

1. OBJECTIVES 1. 2. 3. HW REMINDERS SIMULATIONS HW DISCUSSION STUDY FOR QUIZ CHAPTER 11 QUIZ TOMORROW

5. Someone hands you a coin, and tells you it is biased towards landing heads. As a good stat student, you are skeptical. What would you do?

6. 1. Conduct a simulation on your calculator. randInt(0, 1) (0 = TAILS, 1 = HEADS) 2. randInt(0, 1, 5) Mess with this - do you get any that are all heads / tails? 3. sum(randInt(0, 1, 100)) 4. Make your decision: What would it take to convince YOU that the coin is biased? 1 FLIP 5 FLIPS 100 FLIPS, COUNT # OF HEADS

7. We will never know the truth for sure..... ** A fair coin could come up as 75 heads out of 100. ** A biased coin could come up as a 50 - 50 split. "Such is the nature of Statistics - the branch of mathematics in which we never know exactly what we are talking about or whether anything we say is true."

8. Suppose a basketball player has an 80% free throw success rate. How do we use a simulation to simulate whether or not she makes a foul shot? COMPONENT: (most basic event we are simulating) TRIAL: (Sequence of events we want to investigate) RESPONSE VARIABLE: (What we want to measure / count) STATISTIC: (taking the mean....)

9. How many shots might she be able to make in a row without missing? Describe the simulation of having her shoot free throws until she misses, counting the number of successes. COMPONENT: (most basic event we are simulating) TRIAL: (Sequence of events we want to investigate) RESPONSE VARIABLE: (What we want to measure / count) STATISTIC: (taking the mean....)

10. How would our simulation procedure change if she was only a 72% free throw shooter? COMPONENT: (most basic event we are simulating) TRIAL: (Sequence of events we want to investigate) RESPONSE VARIABLE: (What we want to measure / count) STATISTIC: (taking the mean....)

11. How would a trial and our response variable change if we wanted to know how many shots she might make out of 5 chances she gets at a crucial point in the game? COMPONENT: (most basic event we are simulating) TRIAL: (Sequence of events we want to investigate) RESPONSE VARIABLE: (What we want to measure / count) STATISTIC: (taking the mean....)

12. How would a trial and our response variable change if we want to know her chances of hitting both shots when she goes to the line to shoot two? COMPONENT: (most basic event we are simulating) TRIAL: (Sequence of events we want to investigate) RESPONSE VARIABLE: (What we want to measure / count) STATISTIC: (taking the mean....)

13. How would the simulation change if we want to know her score in a 1-and-1 situation. (She gets to try the second only if she makes the first). COMPONENT: (most basic event we are simulating) TRIAL: (Sequence of events we want to investigate) RESPONSE VARIABLE: (What we want to measure / count) STATISTIC: (taking the mean....)

14. We are to randomly select 3 students from the class to speak at Parents' Night about the joys of taking AP Stat. How likely is it that we'll get 3 boys? COMPONENT: (most basic event we are simulating) TRIAL: (Sequence of events we want to investigate) RESPONSE VARIABLE: (What we want to measure / count) STATISTIC: (taking the mean....)