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Formulas: ο Bayesβ π π΄π πΈ = π(π΄π )βπ(πΈ|π΄π ) π(πΈ) when ο π(π) = π(π¨π ) β π· π¬ π¨π + π(π¨π ) β π· π¬ π¨π + β― + π(π¨π ) β π· π¬ π¨π π π ππ β ππβπ ο Bernoulli b(n,k;p)= ο Expected Value πΈ = π1 β π1 + π2 β π2 β¦ β¦ . . +ππ β ππ ο W-up : for #1-4 Use the tree to answer the following questions purple K white 3 4 purple L 5 11 1. 2. 3. 4. P(W|K) P(Y|L) P(white) P(K|W) 5. Find the probability of throwing a sum of 10 in at least 3 times in 5 throws of a pair of dice? white yellow 6. Three Machines A1, A2, A3, produce 55%, 30%, and 15% of total production. They produce 1%, 2%, and 3% defective output respectively. An item chosen at random is defective. What is the probability that it came from A2? ο 7. Colleen bets $1 on a 2-digit number. She wins $75 if she draws her number from the set of all 2 digit numbers {00,01,02,03β¦99}; otherwise she loses her $1. ο A) is this game fair to the player? ο B) how much is Colleen expected to lose in a game? W-up: ch 9 1. Use calculator to find mean, population and sample standard deviation Class Frequency 7-10 5 11-14 11 15-18 2 19-22 7 SHOW STEPS β WORK!! For 2 -4 Given the sample data, 5, 9, 10, 11, 14 find 2. Mean 3. Standard deviation 4. Z-score for 9 5. Find the area between - .75 and 1.65 standard deviation 6. Find the area that exceeds 1.85 standard deviations ο 7. the weight of 100 college students closely follows a normal distribution with a mean of 130 pounds and a standard deviation of 5.2 pounds. ο A) draw a normal bell curve to 3 standard deviations ο B) how many students would you expect to weigh at least 142 pounds? ο C) what range of weights would you expect to include the middle 70% of students in this group? 1. 4/7 2. 3/11 3. .4837 4. .2953 Answer to 5 5 1 3 11 2 5 1 5 11 0 5 1 4 11 1 ( )( ) ( ) + ( )( ) ( ) + ( )( ) ( ) = 3 12 12 5 12 12 4 12 12 .005 ο 6. Answer: π π΄2 π· = ο= .006 .016 .3 (.02) .55 .01 +.3 .02 +.15(.03) = .375 ο 7. NO the game is not fair ο She expects to loose 25cents per ticket on average in the long run Ch 9 answers 1. 14.26 4.48 4.39 2. 9.8 3. 3.27 (want sample standard deviation) 4. -0.245 5. 0.7239 6. .0322 7. is # 17 on 9.6 Ch 8: Rev: 1-35 Odds are fair game!! 9.5 β standard deviation by hand 1-5 Standard deviation for grouped data using calculator 15 9.6 normal distribution z-scores, how to read chart, one story prob 11-14,17