QBA201 Quantitative Business AnalysisAssignment-4Due Monday, April 25, 2016Instructor: Iker KayaPlease 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.Questions1. (15 Points) The number of midterm exams taken per semester by AUS students is normallydistributed 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 ofmidterms 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 normallydistributed with a mean of 26 minutes and a standard deviation of 10 minutes. There are a totalof 200 students in the professor’s classes. What is the probability that he needs more than 80hours to mark all the midterm exams? (The 200 midterm exams of the students in this year’sclasses can be considered a random sample of the many thousands of midterm exams theprofessor has marked and will mark.)3. (14 Points) A car dealer in Dubai claims in an advertisement that 3% of all its cars require aservice in the first year. An SBM student who takes the QBA class wants to check the claim bysurveying 400 people who recently purchased one of the dealer’s cars. What is the probabilitythat more than 4.7% require a service within the first year? What would you say about theadvertisement’s honesty if in a random sample of 400 people 4.7% report at least one servicecall?4. (14 Points) Among the most exciting aspects of a student’s life are the important calls theymake where such critical issues as the make and model of the car he will purchase and whethershe 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. Theresponses are listed here. Assuming that the variable is normally distributed with a standarddeviation of 8 hours, estimate the mean number of hours spent on those calls by all students. Usea confidence level of 90%.14173617384201579051115181384QBA201 Quantitative Business AnalysisAssignment-45. (14 Points) A statistics professor wants to compare today’s students with those 5 years ago. Allhis current studentsâ grades are stored on his computer so that he can easily find the populationmean. However, the grades 5 years ago are in a random file in his computer. He does not want toretrieve all the grades and will be satisfied with a 95% confidence interval estimate of the meangrade 5 years ago. If he assumes that the population standard deviation is 12, how large a sampleshould 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 statisticscourse was drawn. At the course’s completion, each student was asked how many hours he or shespent doing the homework in statistics. The data are listed here. It is known that the populationstandard deviation is σ =16. The instructor has recommended that students devote 6 hours perweek for the duration of the 12-week semester, for a total of 72 hours. Test to determine whetherthere is evidence that the average student spent less than the recommended amount of time.Compute the p-value of the test.6280526072765880766070767. (14 Points) A smartphone manufacturer advertises that, on average, its cell phone batterieswill last more than 50000 hours. To test the claim, an AUS student took a random sample of 100smartphones and measured the amount of time until each battery lasted. Mean for the sample is50650. If we assume that the lifetime of this type of battery has a standard deviation of 4000hours, can we conclude at the 5% significance level that the claim is true?