STAT302 Secs 102 103 Summer I 1998 Exam 2 Form A Instructor Julie Hagen Carroll 1 Don t even open this until you are told to do so 2 Be sure to mark your section number and your test form on the scantron 3 Sign your name where indicated on your scantron and write your Wednesday section number and computer number beside it Also you must place your scantron in the correct section stack for next Wednesday 4 There are 20 multiple choice questions on this exam each worth 5 points There is partial credit Please mark your answers clearly on the scantron Multiple marks will be counted wrong 5 You will have 60 minutes to finish this exam 6 If you are caught cheating or helping someone to cheat on this exam you both will receive a grade of zero on the exam You must work alone 7 This exam is worth 100 points and will constitute 20 of your final grade 8 Good luck 1 STAT302 102 103 Exam 1 Form A 6 What is z such that P z Z z 0 75 and Z N 0 12 1 What affects the sampling distribution of the sample mean X A B C D E A whether the sample is random or not B the size of the sample n C the parent population distribution the population being sampled D All of the above affect the sampling distribution of X E Exactly two of the above affect the sampling distribution of X A B C D E N 8 11 22 N 8 52 N 8 252 N 8 52 N 8 52 A B C D E A It is the only continuous distribution mentioned B Any data can be well approximated by the normal distribution C Any sample mean X distribution can be well approximated by the normal distribution D Even the sample proportion p distribution can always be well approximated by the normal distribution E None of the above are true 1 and sX 0 4 1 and sX 1 16 1 and sX 2 6 1 and sX 1 265 1 6 and sX 2 6 4 For the X distribution above what is P X 2 A B C D E 0 2 0 1 0 5 0 3 0 10 For Z N 0 1 what is P Z 0 65 A B C D E 5 What is z such that P Z z 0 075 and Z N 0 12 A B C D E 1 6838 0 2662 0 6838 0 2912 0 9750 9 Why is the normal distribution so important in Statistics 302 3 What are the mean X and standard deviation sX for the distribution represented in the table above X X X X X N 0 3 0 0772 N 0 3 0 00062 N 0 3 0 032 N 0 3 0 072 We can t say it is normal since n 6 30 8 For Z N 0 1 what is P 0 55 Z 1 96 X 0 1 2 4 p X 0 5 0 2 0 2 0 1 A B C D E 0 675 1 15 0 7734 0 75 1 75 7 If the true population proportion 0 3 what is the approximate sampling distribution of the sample proportion p for samples of size n 35 2 If X N 3 52 and Y 7 5X what is the distribution of Y A B C D E Summer I 1998 0 53 1 44 0 47 1 44 0 7734 0 2578 0 7422 0 39 0 39 0 35 11 For X N 3 22 what is P X 0 65 A B C D E 2 0 2578 0 7422 0 88 0 12 0 35 Exam 1 Form A STAT302 102 103 12 If X 25 N 2 52 what is P X 25 1 75 A B C D E 17 Which of the following is are FALSE concerning two events A and B 0 9599 0 0885 0 9115 0 4801 0 5199 A If A and B are mutually exclusive then P A and B 0 B If A and B are mutually exclusive then P A and B P A P B C If A and B are independent then P A B P A D All of the above are true E Exactly two of the above except D are false 13 What is x such that P X x 0 94 if X N 2 52 A B C D E 1 555 9 775 3 555 8 11 0 8264 18 For p50 N 0 5 0 0712 what is P p50 0 6 A B C D E 14 The Central Limit Theorem tells us that A The distribution of any sample mean X can be represented by the normal if the sample size n is large enough B The distribution of any sample can be represented by the normal if the sample size n is large enough C The center of any random sample is the sample mean x D All of the above E Exactly two of the above excluding D 19 What is the probability that one is in Group 2 AND makes a C 0 8023 1 0 4404 0 5596 1 04 A B C D E 16 Let X N 12 52 What is the distribution of X 36 Note n 36 A B C D E X 36 X 36 X 36 X 36 X 36 1 408 0 9207 0 0793 0 8554 0 4562 Grades Group A B C D 1 0 05 0 12 0 02 0 10 2 0 14 0 15 0 05 0 04 3 0 09 0 13 0 04 0 07 15 What is z0 15 Remember that P Z z0 15 0 15 and Z N 0 12 A B C D E Summer I 1998 0 38 0 11 0 0418 0 05 0 49 20 What is the probability that one is in Group 3 OR makes an A N 12 5 N 12 1 6 2 N 12 5 6 2 N 2 5 6 2 N 2 52 2 A B C D E 0 33 0 52 0 61 0 0924 0 09 1D 2C 3D 4B 5D 6B 7A 8B 9E 10A 11C 12D 13B 14A 15E 16C 17B 18B 19D 20B 3