Stats 4 Day 11 Homework and Agenda • Homework Due Monday 2/1 • Chapter 16, page 369 • #1-7, #16-18 Agenda: • 1. Do Now and go over practice • 2. A little more practice • 3. Standard Deviation with Expected Value • 4. Practice sheet Tomorrow: SD and GAME The Greedy Pig • Do Now • Your company bids for two contracts. You believe the probability you get contract 1 is 0.8. If you get contract 1, the probability you also get contract 2 will be .2, and if you do not get contract 1, the probability you still get contract 2 is 0.3. Let X be the number of contracts you get. Create a probability model and find the expected value (E(x)=μ) for the number of contracts. Review Practice Worksheet from Yesterday • Presentation Volunteers for Extra Credit A little more practice • In pairs, complete the half sheet Standard Deviation • What did standard deviation measure again? SPREAD! What does standard deviation mean again? • (How far each data point is from the ______________) AVERAGE! • • What if I told you that the expected value (the average of your possible outcomes given their probabilities) for one of our card games is $1.21, but the standard deviation of that expected value is $100, would you still want to play? The Standard Deviation of the Expected Value contributes to the meaning of the Expected Value as a statistic. It tells us more about the data! • • Finding the Standard Deviation of a Random Variable How far does each value deviate from the average (the expected value)?? Outcome Value X Probability P(X) Deviation Squared (X-E(X))2 or (X-μ)2 Standard Deviation: the average (the expected value) of the deviations! • But, we have to make sure the deviations are positive, so we square them • Multiply and add (like before) • Then undo the square (square root)! Steps to Find SD of the Random Variable 1. 2. 3. 4. 5. 6. Make Probability Model Calculate E(X) (aka μ), the expected value Add Deviations column to table and Calculate the deviations, X-E(X) Square the deviations and multiply by their probabilities Add Square Root Practice 1: our Do Now • • Your company bids for two contracts. You believe the probability you get contract 1 is 0.8. If you get contract 1, the probability you also get contract 2 will be .2, and if you do not get contract 1, the probability you still get contract 2 is 0.3. Let X be the number of contracts you get. Create a probability model and find the expected value (E(x)=μ) for the number of contracts. Find the Standard Deviation! Practice 1 • I invested $30,000 in a company this year. There is a 1% chance they fail and I lose my money, there is a 55% chance that I make a 10% return (that I make $3,000), the remaining percent of the time I will likely make a 30% return (that is, I will make $9,000). What is my expected value for my return and what is the standard deviation? Practice half sheet

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# Due Monday 2/1