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210-peters-07sp02-vB - Math 210 — Topics in Finite Math...

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Unformatted text preview: Math 210 — Topics in Finite Math Spring 2007 — Midterm 2 Name: TA: VERSION B (a) The exam has 4 problems. (b) Show your work for every problem. Answers without justification will not receive credit. ((3) Calculators are not allowed. (d) There is a blank page at the end of the exam for if you need it. Points. Score 2 E O 1. (20 points) An urn contains 3 balls, 1 yellow and 2 blue balls. We repeatedly draw a ball from the ' um and put it back (let us say we do this n times). Let X be the random variable that counts the number of blue balls. (a) What is the expected number of blue balls, what is the standard deviation? (in your answer, both should depend on n) (b) Suppose that n = 12, what is the exact probability that X = 3? (c) What is the smallest number n for which random approximation is valid? (d) Now let n = 18, and use random approximation to compute the chance that X is 10 or 11. l 2. (20 points) The Mangabey—Resort in Cameroon has a large number of Mangabey monkeys. 40% of them are Grey—Cheeked Mangabeys (half of them female and half of them male), 40% are Black I Mangabeys (two—third of them female and one—third male), and 20% are Red—Capped Mangabeys (again two-third female and one-third male). If you pick one of the monkeys at random and it turns out to be a male monkey, what is the chance that it is a Grey—Cheeked Mangabey? 3. (20 points) The average length of a Red-Tailed Monkey is 450m, and the standard deviation is 20m. What is the Chance that the length of a randomly selected Red—Tailed Monkey is at most 480m? 4. (20 points) How many words of 4 or 5 letters can one make With the letters of the word ”monkey" '3 [Note that the words do not have to be actual English words] 5. (20 points) Use the matrix—method to find all solutions of the following equations: m+y+z=8 2x+y=0 a:-2y——z=0. \\ TABLE A.1 Areas under the Standard Normal Curve _ W z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 WW” (3.0 .0000 .0040 .0080 .0120 .0160 .0199 .0239 .0279 .0319 .0359 0.1 .0398 .0438 .0478 .0517 .0557 .0596 .0636 .0675 .0714 .0753 0.2 .0793 .0832 .0871 .0910 .0948 .0987 .1026 .1064 .1 103 .1 141 03 .1179 .1217 ,1255 .1293 .1331 .1368 .1406 .1443 , .1480 .1517 0.4 .1554 .1591 .1628 ' .1664 .1700 .1736 .1772 .1808 .1844 .1879 0.5 .1915 .1950 .1985 .2019 .2054 .2088 .2123 .2157 .2190 .2224 0.6 .2257 .2291 .2324 .2357 .2389 .2422 .2454 .2486 .2517 .2549 0,7 .2580 .2611 .2642 .2673 .2704 .2734 .2764 .2794 ' .2823 .2852 0,3 .2881 .2910 .2939 .2967 .2995 .3023 .3051 .3078 .3106 .3133 0,9 .3159 .3186 ' .3212 .3238 .3264 .3289 .3315 .3340 .3365 .3389 1 _o .3413 .3438 .3461 .3485 .3508 .3531 - .3554 .3577 .3599 .3621 1.1 .3648 .3665 .3686 .3708 .3729 .3749 .3770 .3790 .3810 .3830 1,2 .3849 .3869 .3888 .3907 .3925 .3944 .3962 .3980 .3997 .4015 1.3 .4032 .4049 .4066 .4082 .4099 .4115 .4131 .4147 .4162 .4177 1,4 ' .4192 .4207 .4222 .4236 .4251 .4265 .4279 .4292 .4306 .4319 1,5 - .4332 .4345 .4357 .4370 .4382 .4394 .4406 .4418 .4429 .4441, 1,5 .4452 .4463 .4474 .4484 .4495 .4505 .4515 .4525 .4535 .4545 , 1.7 .4554 .4564 .4573 .4582 .4591 .4599 - .4608 .4616 .4625 .4633 1,3 .4641 .4649 .4656 .4664 .4671 .4678 .4686 .4693 .4699 .4706 1,9 .4713 .4719 .4726 .4732 .4738 .4744 .4750 .4756 .4761 .4767 2.0 .4772 .4778 .4783 .4788 .4793 .4798 .4803 .4808 .4812 .4817 2.1 .4821 .4826 .4830 .4834 .4838 .4842 .4846 .4850 .4854 .4857 2.2 .4861 .4864 .4868 .4871 .4875 .4878 .4881 .4884 .4887 .4890 23 ..4893 . .4896 .4898 .4901 .4904 .4906 .4909 ' .4911 .4913 .4916 2.4 .4918 .4920 .4922 .4925 .4927 .4929 .4931 .4932 .4934 .4936 2.5 .4938 .4940 .4941 .4943 .4945 .4946 .4948 .4949 .4951 .4952 25 .4953 .4955 .4956 .4957 .4959 .4960 .4961 .4962 .4963 .4964 2.7 .4965 .4966 .4967 .4968 .4969 .4970 .4971 , .4972 .4973 .4974 28 .4974 .4975 .4976 .4977 .4977 .4978 .4979 .4979 .4980 .4981 29 .4981 .4982 .4982 .4983 .4984 .4984 .4985 .4985 .4986 .4986 3,0 .4987 .4987 .4987 .4988 .4988 .4989 .4989 .4989 .4990 .4990 W ...
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