1. What do we call the graph of a normal distribution? The graph is symmetric about what vertical line?

2. Holt McDougal Algebra 2 8-8 Analyzing Decisions 8-8 Analyzing Decisions Holt Algebra 2 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz Holt McDougal Algebra 2

3. 8-8 Analyzing Decisions Warm Up 1. rolling 2 and tossing heads when rolling a number cube and tossing a coin Find each probability. 1 12 2. rolling an even number or rolling 5 when rolling a number cube 2 3 3. not choosing a multiple of 11 when randomly choosing a whole number from 0 to 99 9 10

4. Holt McDougal Algebra 2 8-8 Analyzing Decisions Explain that probability can be used to help determine if good decisions are made. Use probabilities to analyze decisions and strategies. Objectives

5. Holt McDougal Algebra 2 8-8 Analyzing Decisions expected value Vocabulary

6. Holt McDougal Algebra 2 8-8 Analyzing Decisions In experiments with numerical outcomes, the expected value (EV) is the weighted average of the numerical outcomes of a probability experiment.

7. Holt McDougal Algebra 2 8-8 Analyzing Decisions

8. Holt McDougal Algebra 2 8-8 Analyzing Decisions Example 1: Finding Expected Value The sides of a six-sided number cube are labeled 1, 1, 3, 3, 9, and 9. Value of Side Probability A. What is the expected value of the number cube? 1 1 6 1 6 1 6 1 6 1 6 1 6 13399

9. Holt McDougal Algebra 2 8-8 Analyzing Decisions Example 1: Continued B. What is the expected value of rolling two number cubes, one labeled as described in part A and the other labeled 1– 6? 2 3 4 1 2 +3 5 6 =7 =7.83 1 1 6 + + + + + E(V)= 1 1 6 3 1 6 3 1 6 9 1 6 9 1 6 +1++ == =1 +339+9 6 26 6 1 3 4

10. Holt McDougal Algebra 2 8-8 Analyzing Decisions Check It Out! Example 1 What is the expected value of rolling the six sided number cube as shown in the net below?

11. Holt McDougal Algebra 2 8-8 Analyzing Decisions Example 2 : Using Expected Value in Real-World Situations EV(south) = 0.8(2) + 0.2(4) = 2.4 EV(east) = 0.6(2.5) + 0.4(3) = 2.7 He should take the southern route. On a mountain, it takes Sam 2 hours to climb the southern route, unless there is ice, which increases the time to 4 hours. It takes him 2.5 hours to climb the eastern route, unless there is ice, which increases the time to 3 hours. If the chance of ice is 20% on the southern route and 40% on the eastern route, which route should Sam take if he wants to finish the climb as soon as possible?

12. Holt McDougal Algebra 2 8-8 Analyzing Decisions Check It Out! Example 2 Jack can take one of three routes to work each day. Route A takes 16 minutes, Route B takes 10 minutes, and Route C takes 20 minutes. There is a 40% chance he will encounter an accident in Route A, which increases travel time to 25 minutes. There is also a 20% chance he will encounter a traffic jam if he takes Route B, which increases his travel time to 40 minutes. He has a 10% chance of experiencing a delay in Route C, which increases his travel time to 32 minutes. Which route should Jack take to work each day?

13. Holt McDougal Algebra 2 8-8 Analyzing Decisions Example 3: The Monty Hall Problem In a TV game show, a car key is hidden in one of five bags. The other bags contain fake keys. Once the contestant picks a bag, the host, knowing where the key is located, opens a bag with a fake key. As the contestant answers questions correctly, he continues to open bags with fake keys until two bags remain: one with the car key and one with a fake key. At this time, he offers the contestant a chance to switch bags. Find the expected value of sticking with the original bag and the expected value of switching bags. EV(sticking) = 1 5 EV(switching) = 4 5

14. Holt McDougal Algebra 2 8-8 Analyzing Decisions Check It Out! Example 3 Mikayla is applying to 3 colleges. She makes estimates of her chances of being accepted, and estimates of her chances of receiving financial aid from each, presented below:

15. Holt McDougal Algebra 2 8-8 Analyzing Decisions Check It Out! Example 3 Continued College A: 0.75 · 0.30 = 0.225 College B: 0.65 · 0.40 = 0.260 College C: 0.70 · 0.45 = 0.315 She has a higher probability of being accepted in College C with a financial aid. At which college is she most likely to be both accepted and receive financial aid?

16. Homework pp. 606-607 6-16