BA201 Quantitative Business Analysis Assignment-4 Due Monday, April 25, 2016 Instructor: Iker Kaya Please place a header on you submission that includes your name, ID and section number (Section 07). You must show your work for all questions to receive full credit. Questions 1. (15 Points) The number of midterm exams taken per semester by AUS students is normally distributed with a mean of 11 and a standard deviation of 3. a. What proportion of students takes more than 13 exams per semester? b. What is the probability that in a random sample of 20 students more than 240 (total number of midterms taken by all 20 students in the sample) midterms are taken? 2. (15 Points) The time it takes for a QBA professor to grade his midterm exam is normally distributed with a mean of 26 minutes and a standard deviation of 10 minutes. There are a total of 200 students in the professor's classes. What is the probability that he needs more than 80 hours to mark all the midterm exams? (The 200 midterm exams of the students in this year's classes can be considered a random sample of the many thousands of midterm exams the professor has marked and will mark.) 3. (14 Points) A car dealer in Dubai claims in an advertisement that 3% of all its cars require a service in the first year. An SBM student who takes the QBA class wants to check the claim by surveying 400 people who recently purchased one of the dealer's cars. What is the probability that more than 4.7% require a service within the first year? What would you say about the advertisement's honesty if in a random sample of 400 people 4.7% report at least one service call? 4. (14 Points) Among the most exciting aspects of a student's life are the important calls they make where such critical issues as the make and model of the car he will purchase and whether she will get a new designer handbag are discussed. A sample of 20 students was asked how many hours per month are devoted to these calls. The responses are listed here. Assuming that the variable is normally distributed with a standard deviation of 8 hours, estimate the mean number of hours spent on those calls by all students. Use a confidence level of 90%. 14 17 3 6 17 3 8 4 20 15 7 9 0 5 11 15 18 13 8 4 QBA201 Quantitative Business Analysis Assignment-4 5. (14 Points) A statistics professor wants to compare today's students with those 5 years ago. All his current students' grades are stored on his computer so that he can easily find the population mean. However, the grades 5 years ago are in a random file in his computer. He does not want to retrieve all the grades and will be satisfied with a 95% confidence interval estimate of the mean grade 5 years ago. If he assumes that the population standard deviation is 12, how large a sample should he take to estimate the mean to within 2 grades? 6. (14 Points) A random sample of 12 second-year AUS students enrolled in a business statistics course was drawn. At the course's completion, each student was asked how many hours he or she spent doing the homework in statistics. The data are listed here. It is known that the population standard deviation is =16. The instructor has recommended that students devote 6 hours per week for the duration of the 12-week semester, for a total of 72 hours. Test to determine whether there is evidence that the average student spent less than the recommended amount of time. Compute the p-value of the test. 62 80 52 60 72 76 58 80 76 60 70 76 7. (14 Points) A smartphone manufacturer advertises that, on average, its cell phone batteries will last more than 50000 hours. To test the claim, an AUS student took a random sample of 100 smartphones and measured the amount of time until each battery lasted. Mean for the sample is 50650. If we assume that the lifetime of this type of battery has a standard deviation of 4000 hours, can we conclude at the 5% significance level that the claim is true