BASIIS Total Score : 30 Course Title: Probability and Statistics Time allowed: 90 Minutes Instructors: Dr. Emad Yacoub & Dr. El-Amira Hend Said. The Exam Contains 4 Questions in TWO Pages. Programmable & Graphical Calculators are NOT allowed. Answer all questions: Be sure to write each question number and part number ahead of your answer. Question 1: (8 Marks) (A) Justify the True and correct the False of the following statements: (4 Marks) 1. A student scored in the 85th percentile on a standardized test. This means that the student scored lower than 85% of all students who took the test. 2. Percentiles divide a distribution into 10 equal parts. 3. As the coefficient of variation increases, risk decreases. 4. Suppose the events A and B are such that P(A UB) = 0.8 and P (AnB) = 0.4. Then P (B) = 0.4 (B) A large firm has 85% of its service calls made by a contractor, and 10% of these calls result in customer complaints. The other 15% of the service calls are made bt their own employees, and these calls have 5% complaint rate Find (i) The probability of receiving a complaint. (2 Marks) (ii) The probability that the complaint was from a customer serviced by the contractor. (2 Marks) Question 2: (6 Marks) During the laying of gas pipelines, the depth of the pipeline (in mm) must be controlled. One service provider recorded depths of: 418 428 431 420 412 425 423 433 417 420 410 431 429 425 (A) Calculate the coefficient of variation. (2 Mark (B) Compute the second quartile, 7th decile and the mode. (2 Mark (C) Measurements by another service provider have a sample mean of 425 and a standard deviation of 6.3 Which provider's set of measurements is relatively more variable? (2 Mark Question 3: (7 Marks) 120 (A) Five people, designated as A, B, C, D. E, are arranged in linear order. Assuming that each possible or is equally likely, what is the probability that O. 21 1 2! (i) There is exactly one person between A and B? (2 Mar (ii) There are exactly two people between A and B? 27272 51 (2 Ma (B) If two events A and B are such that P (A) = 0.5, P (B) = 0.3, and P (An B) = 0.1. find the following (i) P(AUB) (ii) P(AnBAUB) (ii) Are the complement of A and B independent? Why? (3 Ma 4 0.S Page 1 of 2 2 X 2 x2 51 Question 4: (9 Marks) (A) Consider the system diagrammed in Figure (1), which consists of 1 1 components having the reliabilities shown in that figure. Find the probability of success of this system. (3 Marks) 0.8 0.8 0.8 0.8 0.9 0.8 0.9 0.9 0.9 0.9 0.8 Figure (1) (B) An elementary school is offering 3 language classes: one in Spanish, one in French, and one in German. The classes are open to any of the 100 students in the school. There are 28 students in the Spanish class, 26 in the French class and 16 in the German class. There are 12 students that are in both Spanish and French, 4 that are in both Spanish and German, and 6 that are in both French and German. In addition, there are 2 students taking all 3 classes. (i) If a student is chosen randomly, what is the probability that he or she is not in any of the language classes? O - SAX (2 Marks) (ii) If a student is chosen randomly, what is the probability that he or she is taking exactly one language class? (2 Marks) (iii) If 2 students are chosen randomly, what is the probability that at least 1 is taking a language class? (2 Marks) Good Luck