MATH 204 Exam 2, Spring 2005

Name: ID number: Time: 1 hour Math 204 8/04/06 Quiz I Second Semester 05/06 Instructor: Mrs. Muna Jurdak Section | Thurs. 11:00 a.m. Section 2: Fri. 1:00 p.m. Section 3: Thurs. 3:30 p.m. Section 4: Thurs. 2:00 p.m. Instructions: 1. Write your name and ID number clearly where indicated. 2. Circle your section number above, according to the time of the problem solving session in which you are enrolled. 3. Solve the problems on this, the white question sheet. Use the colored sheets for scratch work only. You may use the back of a white sheet to complete the solution of a problem. 4. Give numerical answers correct to 2 decimal places. 5. Show your work in all the problems. 1 2 3 4 5 6 7 8 Total (2 /10 ‘0 AS 8 ‘7 ‘10 /A8& /100 (12%) 1. (a)Find a for y=(e* )in(/x +1 )s x 10+x (41) (b) Find f(1) for f(x) = (c)Use the chain rule to find ay ,ify =¥ol and u =(x? — 3x + 1)". dx u+l a vx (10%) 2. (a) Find [(V/5x + 21x® -1)dx. (b) If g"(x) = = +2, (1) =5 and g(1)=9, find (x). x (10%) 3. The frequency distribution for a random variable X is given below. xX 1 2 3 6 Frequency 40 20 60 80 (a) Construct the probability distribution of X. (b)Find p(X = 2). (c)Find p(X > 6). (15%) 4. The time it takes a college freshman to complete a certain reasoning test is normally distributed, with a mean of 25 minutes and standard deviation equal to 6 minutes. (a)Find the probability that, a student chosen at random, will take between 10 and 20 minutes to finish the test. (b) Find the probability that, a student, chosen at random, will take between 5 and 45 minutes to finish the test. (c) Find the time t; below which only 20% of the students take to finish the test. CHAPTER 14 PROBABILITY DISTRIBUTIONS Rese Area Under the Standard Normal Curve -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 = 1293S 18310 .1368 = 1406) = 1443) £1480) ~3— 1517 0.4 .1554 1591 =.1628: 1664 =.1700 .1736 .1772 .1808 .1844 1879 0.5 .1915 1950 .1985 .2019 .2054 .2088 .2123 .2157 .2190 .2294 0.6 .2257 2291 =.2324 0.2857) 23890 24222454 2486 = 62518 ~— 2549 0.7 .2580 2612 .2642 2673 .2704 27384 .2764 .2794 2823 .2852 0.8 .2881 -2910 .29389 .2967 .2995 .3023 .3051 .3078 3106 .3133 0.9 .3159 3186 .3212 .3238 .38264 .3289 .38315 .3340 .3365 .3389 1.0 3413 3438 .3461 .38485 .3508 .3531 .38554 .38577 ..3599 3621 11 .3643 _.8665 .8686 §=.8708 )= 3729'S 8749S .3770 = 3790 = 3810 ~——.3 830 1.2 ~ .3849 8869 .3888 .3907 .3925 .3944 .3962 3980 .3997 4015 13 .4032 4049 .4066 .4082 .4099 .4115 .4131 .4147 4162 14177 14 4192 4207 .4222 4236 4251 ° .4265 .4279 .4292 4306 .4319 1.5 .4332 4345 .43857 .4870. .4882 .4394 .4406 .4418 .4429 4441 1.6 .4452 4463 .4474 4484 4495 .4505 .4515 .4525 45385 .4545 1.7 .4554 .4564 .4573 .4582 .4591 .4599 .4608 4616 .4625 .4633 18 .4641 4649 .4656 .4664 4671 .4678 4686 .4693 4699 .4706 19 .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 2.3 .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 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 A975 .4976 .4977 4977 .4978 .4979 .4979 .4980 .4981 2.9 14981 4982 .4982 4983 .4984 .4984 .4985 .4985 4986 4986 “3.0 49865 4987 .4987 .4988 .4988 .4989 .4989 .4989 4990 .4990 SS eS SSS SSS SSS Area = 0.3413 Area = 0.3413 (8%) 5. A box contains 4 red balls and 6 white balls. An experiment consists of drawing 5 balls at random from the box, with replacement. Find the probability that at least 3 of the balls are red. (17%) 6. Of 120 students, 60 are studying French, 50 are studying Spanish, and 20 are studying both French and Spanish. (a)A student is chosen at random. Find the probability that: (i)The student is studying neither French nor Spanish. (ii) The student is studying exactly one of the two languages. (iii)The student is studying French, given that he is studying Spanish. (b) Let F be the event that the student is studying French, and S be the event that the student is studying Spanish. Are F and S statistically independent events? Give a clear reason for your answer. (10%) 7. The scores on a quiz for a class of 40 students have a mean equal to 75 and a standard deviation equal to 9. If the teacher decides to raise each student's grade by 2 grades (a) What will be the new mean (of the raised grades)? Justify your answer. (b) What will be the new standard deviation? Justify your answer. (18%) 8. A pair of dice, one red, one green, is rolled once. The random variable X is the maximum of the 2 numbers obtained on the faces of the dice. (a)If A is the event that X = 3, list the set of outcomes belonging to this event. (b) Find the probability that X < 3. (c) Find the probability that X #3. (d) Let A be the event that X = 3, B be the event that X is even, and C be the event that X> 4. (i)Are the events A, B and C mutually exclusive? Justify your answer. (ii) Are the events A, B and C collectively exhaustive? Justify your answer.