Stats3 Day 1 Chapter 11- using random # table

Do Now Read Handout

Randomness Statistics: See past the randomness and find patterns and relationships in observations Rely on randomness to avoid biases

Modeling Continue with modeling, but now… Simulation Models

Coin Flipping If someone handed you a coin and told you it’s biased to landing on heads, what would you do? Experiments! How many times are enough? Would 3 heads in a row convince you? Why not? Imagine we did 100 trials, would 54/100 heads convince you? 60? What number would convince you? When determining simulation models, we need to think about number of experiments When determining simulation models, we need to think about considering what is “usual” What about 95/100?

Random # Table What if we wanted to model the situation but didn’t have coins? We only have dice… What if we didn’t have either? Or what if we needed more than 6 outcomes? We know there are only two outcomes (heads or tails), so we determine half(1/2) the numbers to be 1 outcome (heads) and half the numbers to be the other outcome (tails). Random Number Table!! Designate numbers (0-9, 00-99, etc,) to be a certain outcome.

Using Random #s Let’s generate some trials for coin flipping using the random number table! 1. What are our possible outcomes? 2. What numbers should we designate for our outcomes? 3. Determine simulation response. 4. How many trials? 5. Analyze by taking average.

Another Example Derrick Rose has an 80% free throw success rate. How can we use random numbers so simulate whether or not he makes a foul shot? How many shots might he be able to make in a row without missing? 1. Determine which numbers (0-9) represent success (a good shot) and fail (a miss) 2. Simulate shooting until you reach a “miss” for a number of trials 3. Mean number of shots made

How does the simulation change if his free throw percentage was 72% How would it change if we wanted to know how many shots he might make out of 5 chances? How would it change if we want to know his chances of making both shots? What if it was a 1-and-1 situation?

Steps for Simulations 1. Identify the component to be repeated 2. Explain how you will model the outcome 3. Explain how you will simulate the trial 4. State response variables 5. Run several trials 6. Analyze 7. State your conclusion There is a competition for $250 grocery gift card at Jewel. They are placing 1 card of 3 variations in cereal boxes. 20% have card A, 30% card B, and 50% card C. If you get all 3 you could win $250 gift card. We want to use a simulation to give us insight into how many boxes of cereal we need to open until we get all 3 cards. Cereal box selection 0,1 = card A 2,3,4= card B 5,6,7,8,9=card C # of boxes to get “success” Average response

Another Simulation Suppose we randomly select 3 students from class to speak at RCPU about how awesome Stats is. How likely is it that it will be all boys? (consider the gender ratio of our class)

Exit Ticket

Homework Chapter 11 #9, 11, 12, 13