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Math 13 Full Name (Print): Summer 2017 Final Exam, Part I 7/19/2017 Time Limit: 75 COA-MATH13-FR-Summer-2017 This exam contains 3 pages (including this cover page) and 13 problems. Check to see if any pages are missing. Enter all requested information on the top of this page, and put your initials on the top of every page, in case the pages become separated. You may use your books, notes, or any calculator on this exam. You are required to show your work on each problem on this exam. The following rules apply: • If you use a “fundamental theorem” you must indicate this and explain why the theorem may be applied. • Organize your work, in a reasonably neat and coherent way, in the space provided. Work scattered all over the page without a clear ordering will receive very little credit. • Mysterious or unsupported answers will not receive full credit. A correct answer, unsupported by calculations, explanation, or algebraic work will receive no credit; an incorrect answer supported by substantially correct calculations and explanations might still receive partial credit. • If you need more space, use the back of the pages; clearly indicate when you have done this. Do not write in the table to the right. Problem Points Score 1 20 2 20 3 20 4 10 5 10 6 10 7 30 8 20 9 15 10 10 11 15 12 10 13 10 Total: 200 Math 13 Final Exam, Part I - Page 2 of 3 7/19/2017 Table 1: Students and missed classes Number of classes missed in a semester Number of Students 0 12 1 5 2 1 3 5 4 7 8 1 1. (a) (5 points) Use the table to calculate the mean and median of number of missed classes. (round up your answer to 4 decimal digits.) (b) (5 points) Create a descriptive graph of your choice to represent the above data. (c) (10 points) Create a five number summary and a Box-Plot. 2. (20 points) Do runners have lower heart rates, on average? Assume that non-runners have an average heart rate of 72 beats per minute. (a) State the null and alternate hypotheses. What is your level of significance? (b) Suppose that we know that = 7 beats per minute. We randomly sample 50 runners and find that X¯ = 68.25 beats per minute. Find the test statistic. (c) Would it be likely to see X¯ = 68.25 (or less) if µ = 72? Explain. (d) If we decide to reject could we be doing this in error? 3. (20 points) An unfair coin is flipped 11 times. For this coin, the probability of heads is 0.7. Use proper notation in answering the questions. (a) What is the probability of getting exactly three heads? (b) What is the probability of getting at most two heads? (c) What is the probability of getting at least seven heads? (d) What is the probability of getting no heads? 4. (10 points) According to ”Jobs Daily” only 0.0018 of applications lead to a job o↵er, how many job applications one needs to be at least %90 sure that at least one leads to a job o↵er? 5. (10 points) Estimate the population mean, µ, using the given sample statistics; Sample statistics: ↵ = 0.04 = 2.15, ¯x = 21.8, n = 32 6. (10 points) The mean height of women in a country (ages 20 29) is 63.9 inches. A random sample of 50 women in this age group is selected. What is the probability that the mean height for the sample is greater than 64 inches? Assume = 2.93 7. (30 points) Only when a fair red dice is rolled higher than 4 then a coin is flipped, if the coin flips a head, then a fair blue dice is rolled. If x is representing the sum of the red and blue dice, then ; (a) Compute the probability distribution function for P r(x = r), as r = 1..12. (b) Compute µ(x). (c) Compute (x). Math 13 Final Exam, Part I - Page 3 of 3 7/19/2017 Table 2: Table for problem 7. Institution A B C D/F Military 27 42 23 21 Religious 16 48 27 19 Media 18 28 40 28 8. (20 points) Describe with examples the di↵erences between disjoint and independent events. Include examples of two dependent disjoint events, and two independent non-disjoint events. 9. (15 points) The times per week a student uses a lab computer are normally distributed, with a mean of 7.5 hours and a standard deviation of 1.5 hours. A student is randomly selected. Find the following probabilities. (a) Find the probability that the student uses a lab computer less than 5 hours per week. (b) Find the probability that the student uses a lab computer between 6 and 8 hours per week. (c) Find the probability that the student uses a lab computer more than 9 hours per week. 10. (10 points) Use the central limit theorem to find the mean and standard error of the mean of the indicated sampling distribution. Then sketch a graph of the sampling distribution. The per capita consumption of Soy beans by people in a country in a recent year was normally distributed, with a mean of 11 pounds and a standard deviation of 3.7 pounds. Random samples of size 15 are drawn from this population and the mean of each sample is determined. 11. (15 points) The contingency table shows how a random sample of college freshmen graded the leaders of three types of institutions. At ↵ = 0.10, can you conclude that the grades are related to the type of institution? 12. (10 points) A child psychologist wants to estimate the mean age at which a child learns to talk using a confidence interval. Find the sample size necessary for a 95% confidence interval with maximal error estimate 4 weeks for the mean age at which a child learns to talk. Assume = 25 weeks. 13. (10 points) Big Shoulders Insurance Company took a random sample of 50 insurance claims paid out during the last year and found that the mean was $1500 and the standard deviation was $120. a. Find and interpret a 95% confidence interval for the parameter of interest. b. The industry standard for last year was an average claim of $1575. Based on your interval computed above, does it appear that Big Shoulders claims are above average? Explain.