Stats 10 - Midterm 2 Spring 2014VERSION 1NAME:SECTION:Academic Misconduct:• Any potential violation of UCLA’s policy on academic integrity will be reported to the officeof the Dean of Students. All work on this exam must be your own.Multiple Choice• On your Scantron sheet write your name, ID, lecture and section letter and TEST Version (fill in thebubbles).• Enter all answers on the scantron sheet (those not recorded on the scantron will NOT be graded).• Choose only ONE answer for each question.• No partial credit will be given for multiple choice.Calculators• You may use a calculator, but you may NOT share with your neighbor.• Cell phones, iPods or other Internet connected devices are NOT allowed to be used as calculators.Other Test Instructions• You are allowed note sheet (8.5 x 11”) with writing on BOTH sides.• Show all your work for the open ended question in order to get credit.• Write clearly. Short answers are best.GOOD LUCK!1. Lauren takes the Santa Monica Big Blue Bus #1 to make the 2nd Stats midterm. Lauren has a historyof missing the bus and today she is running behind. Historically, she has 65% chance of the catching thebus otherwise she ends up running all the way to school. If she misses the bus today she has a 95% ofbeing late to the exam. If she catches the bus she will have a 75% chance of being on time.(a) Lauren was on time for the exam. What is the probability she ran all the way to school? Show yourwork for full credit. [5](b) If Lauren makes the bus what is the probability she is late? [1]22. The next Stats 10 quiz will have six questions; each with four choices (A, B, C, D) and only one correctanswer.X 0 1 2 3 4 5 6P(X) 0.1780 0.3560 0.2966 ? 0.0330 0.0044 ?(a) Complete the above binomial probability table for the values with question marks. [2](b) What is the probability of getting 4 or more correct? Show your work. [2](c) What is the probability you get one correct given that you know you got less than two correct? Theprobability statement is P(X = 1|X < 2). [3](d) Now what if instead I change the quiz to have 115 questions (how horrible would that be?); eachquestion with five choices (A,B,C,D,E) and only one correct answer. 115 questions seems like way,way too many so you decide to randomly guess on each one. What is the probability you get 30 ormore correct? You do not need to check conditions here. [4]3On April 28, 2014 SurveryUSA asked 499 Los Angeles residents about comments made by Los Angeles Clippersowner, Donald Sterling, questioning whether the comments are seen as both offensive and racist. The firstquestion asked, “ Do you find the comments made by Sterling to be offensive, or not offensive.” and theresponses by gender are listed in the table below. (questions 1-3).Male FemaleOffensive 212 190Not Offensive 39 29Not Sure 8 211. What percent of respondents are male and think Donald Sterling’s comments are offensive? Choose theclosest answer.(a) 81.53%(b) 52.74%(c) 42.48%(d) 7.82%2. What percent of respondents who are female think Sterling’s comments are not offensive? Choose theclosest answer.(a) 79.17%(b) 42.65%(c) 12.08%(d) 5.81%3. What percent of respondents are male or think Sterling’s comments are offensive? Choose the closestanswer.(a) 81.85%(b) 42.48%(c) 89.97%(d) 52.74%4. In the game of roulette, a wheel is spun. A small ball is dropped onto the wheel and eventually comes torest in one of 38 slots. There are 3 possible outcomes: the ball lands in odd numbered slot (probability18/38), the ball lands in a even slot (18/38) or the ball lands on 0 or 00 slot (2/38). A gambler at a casinonotices that the last 6 spins have all been even. The probability that the 7th spin is even is:(a) Cant tell because the outcomes of the games have variation(b) Exactly 18/38(c) More than 18/38(d) Less than 18/3845. In a recent survey of 180 random Americans, 9% responded they were unemployed. Choose the answerbelow that is the 90% confidence interval for the proportion of Americans who are unemployed.(a) (0.055, 0.125)(b) (0.032, 0.148)(c) (0.069, 0.111)(d) (0.081, 0.099)6. In a recent survey of 180 random Americans, 9% responded they were unemployed. The 99% confidenceinterval for the proportion of Americans who are unemployed is (0.035, 0.145). What is the appropriateinterpretation of the 99% confidence interval.(a) We are 99% confident that the true proportion of Americans who are unemployed is between 3.5%and 14.5%(b) We are 99% confident that the sample proportion of Americans who are unemployed is between 3.5%and 14.5%(c) There is 99% chance that the true proportion of Americans who are unemployed is between 3.5%and 14.5%(d) There is 99% chance that the sample proportion of Americans who are unemployed is between 3.5%and 14.5%7. In a random sample of UCLA students, if the probability that a student has travelled to Canada is 1/3, theprobability that a student has travelled to Mexico is 3/5 and the probability that a student has travelledto both Mexico and Canada is 1/5. Are the events of traveling to Mexico and Canada:(a) Disjoint(b) Dependent(c) Neither(d) Both8. 90% of Americans have had chicken pox by the time they reach adulthood. In a random sample of 3American adults, what is the probability that exactly 1 person has had chicken pox?(a) 0.027(b) 0.90(c) 0.009(d) 0.279. 90% of Americans have had chicken pox by the time they reach adulthood. According to the CentralLimit Theorem, the sample proportion of random sample of size 50 will be distributed approximatelynormal?(a) True(b) False510. A “social experiment” conducted by a TV program questioned what people do when they see a veryobviously bruised woman getting picked on by her boyfriend. On two different occasions at the samerestaurant the same couple was depicted, where in one scenario the woman was dressed “provocatively”and in the second scenario the woman was dressed “conservatively”. The contingency table below showshow many restaurant diners were present under each scenario, and whether or not they intervened.Provocative Conservative TotalIntervened 4 16 20Did Not Intervene 16 9 25Total 20 25 45We use simulation to test if how the woman is dressed is associated with whether or not people intervened.We write “yes” on 20 index cards and “no” on 25 index cards to indicate whether or not a diner (representedby each card) intervened. We next shuffle the cards and deal them into two groups of size 20 and 25, theprovocative and conservative