Download STAT 400 Exam: Probability and Statistics - Prof. Brian R. Hunt and more Exams Probability and Statistics in PDF only on Docsity! STAT 400 Exam Sec. 0701 Final Exam (Tuesday, May 20) Exam ends promptly at 6:00. Exam is open book, open notes; calculators are allowed. Your final answer(s) to each question should be circled, and for full credit you must show your work. Brief verbal explanations of the steps you follow are helpful in earning partial credit. Numerical answers should be simplified to either an exact answer or a decimal answer (as accurate as possible up to 4 decimal places). Any work that you do not want to be considered should be crossed out. 1. (25 points) A company has 12 applicants for a job; let us number them from 1 (most qualified) to 12 (least qualified). Due to time limitations the company selects 4 appli- cants at random to interview, and hires the most qualified of those 4. For example, if applicants 3, 4. 8, arid 10 are selected to interview, then applicant 3 is hired. (a) What is the probability that the most qualified applicant (1) is hired? (b) What is the probability that one of the best 5 candidates (1, 2, 3. 4, or 5) is hired? (c) What is the probability that the second most qualified applicant (2) is hired? If applicant 2 is selected to interview, what is the conditional probability that (s)he is hired? 2. (15 points) A multiple choice exam of 25 questions is answered at random. Assume that each question is answered correctly with probability 1/4, and that each answer is independent of the others. (a) What is the expected number of correct answers? (b) What is the probability that 4 or fewer questions are answered correctly? (c) What is the probability that 5, 6, 7, 8, or 9 questions are answered correctly? (d) What is the proba.bility that 10 or more questions are answered correctly? 3. (25 points) Assume that the number X of vehicles towed per week by a given tow-truck operat ">r is normally distributed with mean 50 and standard deviation 10. Assume that the op -rater's weekly profit is Y - 70X - 2500. (a) What are the mean and standard deviation of Y? (b) What is the probability that a profit is made in a given week? That is, find P(Y > 0). (c) What is the proba.bility that a profit is made in a given two-week period? Assume that the number of cars towed one week is independent of the number towed the following week. (d) Are X and Y independent? Explain briefly. 4. (20 points) The joint probability mass function p(x, y) for two discrete random variables X and Y is given by the following table. Spring 1997 B. Hunt
