Alg2 Notes 8.8.notebook
March 22, 2013
8­8 Analyzing Decisions
Skills we've learned and will be quizzed on TODAY
8.1 Measures of Central Tendency
­ mean, median, mode, variance, standard deviation, expected value, box­and­whisker plot, interquartile range, outlier
8.2 Data Gathering
­ population, census, sample, random sample, convenience samples, and self­selected samples, underrepresented, overrepresented, bias samples, statistic, parameter
8.3 Surveys, Experiments, & Observational Studies ­ experiment, observational study, controlled experiment, treatment group, control group, randomized comparative experiment
8.4 Significance of Experimental Results
­ hypothesis testing, null hypothesis, z­Test, 95% confidence level: If , then you can reject the null hypothesis with 95% certainty. If , then you do not have enough evidence to reject the null hypothesis. 8.5 Sampling Distributions
­ simple random sample, systematic sample, stratified sample, cluster sample, convenience sample, self­selected sample, probability sample, margin of error
8.6 Binomial Distributions
­ binomial theorem, binomial expansion
Oh by the way...
1 standard deviation: 68.2%
2 standard deviations: 95.4%
3 standard deviatons: 99.7%
8­8 Analyzing Decisions
1. Calculate Expected Value
2. Use Expected Value to Make Decisions and Analyze Strategies Your project!
Alg2 Notes 8.8.notebook
March 22, 2013
I. Expected Value
Another way:
Expected Value is the weighted average of the numerical outcomes of a probability experiment.
1. The sides of a six­sided number cube are labeled 1, 1, 3, 3, 9, and 9. What is the expected value of the cube?
2. What is the expected value of rolling a six sided number cube as shown in the net below?
Alg2 Notes 8.8.notebook
March 22, 2013
II. Real World Expected Value
3. 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?
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.
4. 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?
Route A: 0.60(16) + 0.40(25) = 9.6 + 10 = 19.6 minutes
Route B: 0.20(40) + 0.80(10) = 8 + 8 = 16 minutes
Route C: 0.90(20) + 0.1(32) = 21.2 minutes
Alg2 Notes 8.8.notebook
March 22, 2013
III. Monty Hall Problem
5.
6. 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.
Expected Value of staying: 1/5
Expected Value of switching: 4/5
Alg2 Notes 8.8.notebook
March 22, 2013
7. 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:
At which college is she most likely to be both accepted and receive financial aid?
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.
IV. Your Calculator
Re­visit 1. The sides of a six­sided number cube are labeled 1, 1, 3, 3, 9, and 9. What is the expected value of the cube?
List 1: x's (values)
List 2: P(x) (probability of each value)
1 Variable Stats L1, L2
Get both average (expected value) & s.d.
why would you want standard deviation? used to apply to z­scores or normal data
compare different distributions
which casino games have greater spreads
Alg2 Notes 8.8.notebook
8.8 p.606 #2, 3, 5 ­ 8, 12, 13, 15, 18, 22, 23, 27 ­ 29
March 22, 2013