Final examination semester 2 academic year 2019-2020 course name: Mathematical statistics for engineers giúp các bạn sinh viên có thêm tài liệu để củng cố các kiến thức, ôn tập kiểm tra, thi cuối kỳ. Đây là tài liệu bổ ích để các em ôn luyện và kiểm tra kiến thức tốt, chuẩn bị cho kì thi học kì. Mời các em và các quý thầy cô giáo bộ môn tham khảo. | HCMC UNIVERSITY OF FINAL EXAMINATION TECHNOLOGY AND EDUCATION SEMESTER 2 - ACADEMIC YEAR 2019-2020 Faculty of Applied Sciences Course name Mathematical Statistics for Engineers ------------------- Course ID MATH132901E Duration 90 minutes. Number of pages 02 pages Open book. Question 1. 10 Three plants manufacture hard drives and ship them to a warehouse for distribution. Plant I produces 54 of the warehouse s inventory with a 4 defect rate. Plant II produces 35 of the warehouse s inventory with an 8 defect rate. Plant III produces the remain- der of the warehouse s inventory with a 12 defect rate. a. What is the probability that a randomly selected hard drive is defective b. Suppose a hard drive is defective. What is the probability that it came from Plant II Question 2. 10 A large lot of tires contains 5 defectives. 4 tires are to be chosen for a car. a. Find the probability that you find at most 2 defective tires before 4 good ones. b. Find the mean and variance of the number of defective tires you find before finding 4 good tires. Question 3. 10 A shipment of 25 integrated circuits ICs arrives at an electronics man- ufacturing site. The site manager will randomly select 4 ICs and test them to see whether they are faulty. Unknown to the site manager 5 of these 25 ICs are faulty. Suppose the shipment will be accepted if and only if at most one of the inspected ICs is faulty. What is the probability this shipment of 25 ICs will be accepted Question 4. 10 Based on extensive data from an urban freeway near Toronto Canada it is assumed that free speeds can best be represented by a normal distribution . The mean and standard deviation reported in the article were 118 km h and km h respectively. a. The posted speed limit was 100 km h. What percentage of vehicles was traveling at speeds exceeding this posted limit b. If five vehicles are randomly and independently selected what is the probability that at least one is not exceeding the posted speed
