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Stat 100 Final Exam Spring 2005 Each problem is worth 20 points. Do one problem per answer sheet, you may use the back if necessary. All work must be shown to receive full credit. 1, Ina group of 20 students, 12 are males and 9 are business majors. Of the 12 males, 7 are business majors. Let A be the event a student is female and B be the event a student is not a business major. a) Draw a Venn diagram depicting these events. b) What is the probability that a randomly selected student is a female non-business major? c) Given that a student selected is male, what is the probability that he is not a business major? d) Are the events 4 and B independent? Justify your answer. 2. According to the US Department of Education, about 30% of the US population over 21 have a bachelor’s degree. In a random sample of 16 people over 21, determine: a) the probability that at least 5 have bachelor’s degrees b) the probability that at most 8 do not have bachelor’s degrees c) the probability that exactly 10 have bachelor’s degrees d) the expected number that have bachelor’s degrees ¢) Use the normal approximation to approximate the probability that out of 120 people over 21, at most 50 have bachelor’s degrees. 3. A student buys a lottery ticket for $1, For every 1000 tickets sold, 2 DVD players will be given away in a drawing. Let X denote the student’s winnings in dollars. a) What is the probability that the student will win a DVD player? b) If each DVD player is worth $200, determine the student’s expected net gain (ie, winnings minus expenditures). 4. Suppose that student verbal scores, X, on the GRE are normally distributed with mean 497 and standard deviation 120, Find: a) P(X > 600) b) the 90" percentile ¢) the proportion of students that scored above 400. 5. The Washington Post recently reported that Washington area commuters spend an average of 69 hours per year in traffic jams and suppose that the standard deviation is 10 hours. Find the probability that the mean annual amount of time spent in traffic in a sample of 50 commuters is: a) greater than 70 hours b) within 5 hours of the population. 6. From a sample of 2100 credit card accounts, 400 have no debts. a) Determine a 99% confidence interval for the population proportion of credit card accounts that have no debis, b) From your result in part (a), what is the conclusion for testing the null hypothesis that the probability of no debts is 15 versus the alternative that the probability of no debts is different from .15 atthe a =.01 level? 
