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X p1 x1 p2 x2 p3 x3 X pi xi AP Statistics, Section 7.2, Part 1 pn xn 2 The Michigan Daily Game you pick a 3 digit number and win $500 if your number matches the number drawn. What is the average winnings? 1st we need to know, For a 3 digit number how many ways can you win? 10 X 10 X 10 = 1000 combinations of 3 digit #s so, 1/1000 or .001 chance of winning X .001(500) .999 0 .50 0 Is this a fair game? .50 AP Statistics, Section 7.2, Part 1 3 The Michigan Daily Game you pick a 3 digit number and win $500 if your number matches the number drawn. If it cost $1.00 to play. X .001(499) .999 1 .499 .999 .50 What is the average PROFIT? -.50 Mean = Expected Value AP Statistics, Section 7.2, Part 1 4 p1 x1 x p2 x2 x 2 X 2 pi xi x 2 X AP Statistics, Section 7.2, Part 1 pn xn x 2 2 5 2 The Michigan Daily Game you pick a 3 digit number and win $500 if your number matches the number drawn. What is the average winnings? (500 .5) .001 2 X 2 0 .5 .999 2 249.50025 .24975 249.75 15.8 Standard dev. / Variance is how much difference there is in the measurements. AP Statistics, Section 7.2, Part 1 6 Draw independent observations at random from any population with finite mean μ. Decide how accurately you would like to estimate μ. As the number of observations drawn increases, the mean x-bar of the observed values eventually approaches the mean μ of the population as closely as you specified and then stays that close. AP Statistics, Section 7.2, Part 1 7 The distribution of the heights of all young women is close to the normal distribution with mean 64.5 inches and standard deviation 2.5 inches. What happens if you make larger and larger samples… AP Statistics, Section 7.2, Part 1 8 AP Statistics, Section 7.2, Part 1 9 Most people incorrectly believe in the law of small numbers. “Runs” of numbers, etc. AP Statistics, Section 7.2, Part 1 10 Exercises: 7.13-7.33 odd x21 AP Statistics, Section 7.2, Part 1 11