210-peters-07sp02-vA

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

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Unformatted text preview: Math 210 — Topics in Finite Math Spring 2007 — Midterm / Z Name: TA: VERSION A Calculators are not allowed. ) b) Show your work for every problem. Answers Without justification Will not receive credit; ) ) There is a blank page at the end of the exam for if you need it. 1‘, (20 points) The Mangabey—Resort in Cameroon has a large number of Mangabey monkeys. 30% ' of them are Grey- Cheeked Mangabeys (half of them female and half of them male), 50% are Black 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 turnsout to be a male monkey, What is the chance that it is a Grey—Cheeked Man-gabey? ‘2. (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 least 42cm? . , :3. (20 points) An urn contains 3 balls, 1 yellow and 2 blue balls. We repeatedly draw a ball from the urn 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) ' ' a (b) Suppose that n = 10, what is the emact probability that X = 3? (c) What is the smallest number 7} for which random approximation is valid? ((1) Now let n = 18, and use random approximation to compute the chance that X is 11 or 14. TABLE A.1 Areas under the Standard Normal Curve W z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 0.0 .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 .1103 .1141 0.3 .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 .261 1 .2642 .2673 .2704 .2734 .2764 .2794 ' .2823 .2852 0.8 .2881 .2910 .2939 .2967 .2995 .3023 .3051 .3078 .3106 .3133 0.9 .3159 .3186 I .3212 .3238 .3264 .3289 .3315 , .3340 .3365 .3389 1.0 .3413 .3438 .3461 .3485 .3508 .3531 - .3554 .3577 .3599 .3621 1 .1 .3643 .3665 .3686 .3708 .3729 .3749 .3770 .3790 .3810 .3830 1 ,2 .3849 .3869 .3888 .3907 .3925 .3944 .3962 .3980 .3997 _ .401 5 1 ,3 .4032 .4049 .4066 .4082 .4099 .4115 .4131 .4147 .4162 1 .4177 1 .4 ' .4192 .4207 .4222 .4236 .4251 .4265 .4279 .4292 .4306 .4319 1 ,5 .4332 .4345 .4357 .4370 .4382 .4394 .4406 .4418 .4429 I .4441 1 .6 .4452 .4463 .4474 .4484 ‘ .4495 .4505 .451 5 .4525 .4535 .4545 . 1 ,7 .4554 .4564 .4573 .4582 .4591 .4599 ‘ .4608 .461 6 .4625 .4633 1 .8 .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 22 .4861 .4864 .4868 .4871 .4875 .4878 .4881 .4884 .4887 V .4890 2,3 . .4893 .4896 .4898 .4901 .4904 .4906 .4909 .491 1 .4913 .4916 2.4 .491 8 .4920 .4922 .4925 .4927 .4929 .4931 .4932 .4934 .4936 2.5 .4938 .4940 .4941 .4943 .4945 .4946 .4948 .4949 .4951 .4952 2.6 .4953 ' .4955 .4956 .4957 .4959 .4960 .4961 .4962 .4963 .4964 2,7 .4965 .4966 .4967 .4968 .4969 .4970 .4971 » .4972 .4973 .4974 2.8 .4974 .4975 4976 .4977 .4977 .4978 .4979 .4979 .4980 .4981 2.9 .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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210-peters-07sp02-vA - Math 210 — Topics in Finite Math...

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