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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 (twothird of them female and onethird male), and 20% are RedCapped Mangabeys
( again twothird female and onethird 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 Mangabey? ‘2. (20 points) The average length of a RedTailed Monkey is 450m, and the standard deviation is
20m. What is the chance that the length of a randomly selected RedTailed 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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 Fall '08
 WAINGER
 Math, Normal Distribution, Standard Deviation, Variance, Blue Balls, Grey Cheeked Mangabeys

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