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Stat 100 Final Exam Fali 2002 Each problem is worth 20 points. Do one problem per answer sheet. All work must be shown fo receive full credit. 1. In the following cases, a linear relation was found to exist between the given variables. For each case, choose the option (i, ii, or iii) that best describes the relation. a) The GPA and the SAT scores. i) the correlation coefficient r = -.9, ii) the regression line is y = 220 + 91x, iii) the correlation coefficient r = 0 b) The body length and the weight for male wolves. i) the regression line is y = 98 - .04x, ii) the correlation coefficient r = .6, iii) the correlation coefficient r = -.8 c) The age of adults and their ability to maintain a strenuous exercise program. i) the regression line is y = 4x + 2, ii) the correlation coefficient r = .7, iii) the correlation coefficient r = -.6 2. Ina class of 30, 10 wear glasses, 20 are right-handed, and 5 are left-handed and wear glasses. If a student is randomly selected, determine the probability that: a) the student doesn’t wear glasses b) the student is left-handed and doesn’t wear glasses c) the student is left-handed or doesn’t wear glasses. d) Given that the student wears glasses, what is the probability that the student is right- handed? 3. Three coins are tossed. The probability of no heads occurring is .125, the probability of 1 head is 375, the probability of 2 heads is .375, and the probability 3 heads is .125. If an odd number of heads appear, you receive $100. If two heads appear, you receive $75. If no heads appear, you pay $65. Let X denote the dollar amount one wins from playing the game once. a) What is the expected value of the game, E(X)? b) What is the probability of winning at least $75? 4. A report states that 90% of all U.S. citizens have a driver’s license. a) Ina sample of 25 randomly selected U. S. citizens, what is the probability that at most 23 of them have their driver’s licenses? b) In the same sample of 25, what is the probability that between 20 and 25, inclusive, have their driver's licenses? c) Ina sample of 500, what is the approximate probability that at least 460 have their driver’s licenses? 5. A sample of 55 animals of a common breed are injected with adrenaline and their blood sugar levels are recorded. The mean and standard deviation are found to be 126.9 mg/ml and 10.5 mg/ml, respectively. a) Give a point estimate of the population mean b) Find a 95% error margin. c) Determine a 95% confidence interval for the population mean. d) What sample size is needed for a 95% error margin to be 1.3? 
