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The roulette wheel has 38 slots numbered 136 0 and 00

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Unformatted text preview: ove.) iv) (i) Tossing a fair coin 100 times and getting 50%+/ ­ 5% heads (between 45% ­55% heads) (ii) Tossing a fair coin 10,000 times and getting 50% +/ ­ 0.5% heads (between 49.50% and 50.50% heads) Equally likely, both have the same SE% (See table above.) Page 6 Study Guide KEY for Exam 3 Chapter 15—Normal Approximation for Probability Histograms • Probability histograms represent chance by area. • With a large enough number of draws, the probability histogram for the sum, average and percent of draws from a box will follow the normal curve, even when the contents of the box do not. This is the Central Limit Theorem. • The more the contents of the box differs from the normal curve, the more draws are needed before the probability histogram for the sum of the draws looks like the normal curve. • To use the normal curve to figure chances, we must first convert the values to Z scores by subtracting the EV and dividing by the SE. Z = (Value – EV) SE Practice Problems: 1) Look at the 3 boxes and 6 probability histograms below. Each box has 2 probability histograms associated with it. One is the probability histogram for the sum of 2 draws made at random with replacement and the other is the probability histogram for the sum of 20 draws made at random with replacement from the Box. Box A ave= 1 Box B ave=2 Box C ave=5 0 1 2 0 1 5 0 1 14 Under each of the 6 histograms, fill in the first blank with either 2 or 20, and the second blank with either A, B or C. The first one is done for you. __2__ draws from Box __A__ __20__ draws from Box_B __2__ draws from Box_C_ _20___ draws from Box__A_ 20__ draws from Box____ 2_ draws from Box _B_ Sum of 2 draws  compute the largest possible sum for Box A: 2+2=4, Box B: 5+5=10, Box C: 14+14=28, Sum 20 draws—compute the EVsum from A, B, C and you’ll get 20, 40, 100, the middle of the histograms. Page 7 Study Guide KEY for Exam 3 2) A gambler plays roulette 100 times betting \$1 on the numbers 1, 2 and 3 each time. If the ball lands on 1, 2 or 3 the gambler wins \$11, if the ball lands on any of the other 35 numbers the gambler loses \$1....
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