AMS 5 Practice 18 5142017 (8:009:05) Chapter 18, 8, 9, 10, 12, 13, 14, 15 8. A coin is tossed 100 times. True or false, and explain: (a) The expected value for the number of heads is 50. (b) The expected value for the number of heads is 50, give or take 5 or so. (c) The number of heads will be 50. The number of heads will be around 50, give or take 5 or so. 8a) True; [0][1] Avg = , EV = 100*.5 = 50 8b) False, since the EV is a static number 8c) False, see below. 8d) True, since the actual amount of heads drawn will probably fluctuate around 50. 9. One hundred draws are made at random with replacement from a box with ninetynine tickets marked 0 and one ticket marked 1. True or false, and explain: (a) The sum will be around 1, give or take 1 or so. (b) There is about a 68 chance that the sum will be in the range 0 to 2. 9a) True; EV = 100*1100 = 1, SE = 1 9b) False, since you cant apply the normal curve to this data set because theres not enough draws. Needs 400 or more (I suppose). 10. Ten thousand draws are made at random with replacement from a box with ninetynine tickets marked 0 and one ticket marked 1. True or false, and explain: (a) The sum will be around 100, give or take 10 or so. (b) There is about a 68 chance that the sum will be in the range 90 to 110. 10a) True; EV = 10000*1100 = 100, SE = 10

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