STAT302: Secs 102 & 103Summer I 1998Exam #2Fo r m AInstructor: Julie Hagen Carroll1. 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 andcomputer number beside it. Also, you must place your scantron in the correct section stack (for nextWednesday).4. There are 20 multiple-choice questions on this exam, each worth 5 points. There is partial credit. Pleasemark 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 ofzero 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!1STAT302: 102 & 103 Exam #1, Form A Summer I 19981. What affects the sampling distribution of thesample mean, X?A. whether the sample is random or notB. the size of the sample, nC. the parent population distribution (thepopulation being sampled)D. All of the above affect the sampling distri-bution of X.E. Exactly two of the above affect the sam-pling distribution of X.2. If X ∼ N(3, 52)andY =7− 5X, what is thedistribution of Y ?A. N(−8, 11.22)B. N(−8, −52)C. N(−8, 252)D. N(8, 52)E. N (−8, 52)--------------------------------X |0 |1|2|4--------------------------------p(X) | 0.5 | 0.2 | 0.2 | 0.1--------------------------------3. What are the mean, µXand standard deviation,sXfor the distribution represented in the tableabove?A. µX=1andsX=0.4B. µX=1andsX=1.16C. µX=1andsX=2.6D. µX=1andsX=1.265E. µX=1.6andsX=2.64. For the X distribution above, what is P (X>2)?A. 0.2B. 0.1C. 0.5D. 0.3E. 05. What is z∗such that P (Z>z∗)=0.075 andZ ∼ N(0, 12)?A. 0.53B. −1.44C. 0.47D. 1.44E. 0.77346. What is z∗such that P (−z∗<Z<z∗)=0.75and Z ∼ N(0, 12)A. 0.675B. 1.15C. 0.7734D. 0.75E. 1.757. If the true population proportion, π =0.3, whatis the approximate sampling distribution of thesample proportion, p, for samples of size n = 35?A. N(0.3, 0.0772)B. N(0.3, 0.00062)C. N(0.3, 0.032)D. N(0.3, 0.072)E. We can’t say it is normal since n 6=308. For Z ∼ N (0, 1), what is P(0.55 <Z<1.96)?A. 1.6838B. 0.2662C. 0.6838D. 0.2912E. 0.97509. Why is the normal distribution so important inStatistics 302?A. It is the only continuous distribution men-tioned.B. Any data can be well approximated by thenormal distribution.C. Any sample mean, X, distribution can bewell approximated by the normal distribu-tion.D.Eventhesampleproportion,p, distribu-tion can always be well approximated bythe normal distribution.E. None of the above are true.10. For Z ∼ N(0, 1), what is P (Z>0.65)?A. 0.2578B. 0.7422C. 0.39D. −0.39E. 0.3511. For X ∼ N(3, 22), what is P (X>0.65)?A. 0.2578B. 0.7422C. 0.88D. 0.12E. 0.352STAT302: 102 & 103 Exam #1, Form A Summer I 199812. If X25∼ N(2, 52), what is P (X25< 1.75)?A. 0.9599B. 0.0885C. 0.9115D. 0.4801E. 0.519913. What is x∗such that P (X<x∗)=0.94 if X ∼N(2, 52)?A. 1.555B. 9.775C. 3.555D. 8.11E. 0.826414. The Central Limit Theorem tells us thatA. The distribution of any sample mean, X,can be represented by the normal if thesample size, n, is large enough.B. The distribution of any sample can be rep-resented by the normal if the sample size,n, is large enough.C. The center of any random sample is thesample mean, x.D. All of the aboveE. Exactly two of the above (excluding D.)15. What is z0.15? Remember that P(Z>z0.15)=0.15 and Z ∼ N(0, 12)?A. 0.8023B. 1C. 0.4404D. 0.5596E. 1.0416. Let X ∼ N(12, 52). What is the distribution ofX36?Note:n =36A. X36∼ N(12, 52)B. X36∼ N(12, (1/6)2)C. X36∼ N(12, (5/6)2)D. X36∼ N(2, (5/6)2)E. X36∼ N(2, 52)17. Which of the following is/are FALSE concerningtwo events A and B?A. If A and B are mutually exclusive, then P (Aand B)=0.B. If A and B are mutually exclusive, then P (Aand 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.) arefalse.18. For p50∼ N(0.5, 0.0712), what is P (p50< 0.6)?A. 1.408B. 0.9207C. 0.0793D. 0.8554E. 0.4562Grades---------------------------------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---------------------------------19. What is the probability that one is in Group 2AND makes a C?A. 0.38B. 0.11C. 0.0418D. 0.05E. 0.4920. What is the probability that one is in Group 3OR makes an A?A. 0.33B. 0.52C. 0.61D. 0.0924E.