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Part I. Multiple Choice. 3 marks in each question. No part mark. Circle only one answer. If there are more than one correct answer, circle the best one. 1 . A test is given to a sample of 100 students. Suppose the test scores are 25, 64, ..., 35. Calculations show that 25 + 64 +...+ 35 = 3,900 and 252 +64+...+ 35- =166,356. The standard deviation is closest to V (a) 12 (b) 14 (c) 16 (d) 18 (e) 20 2. Let A and B be two events, P(A) = -, P(B | A) = _ and P(A | B) = - . Then P(AWB) is equal to (a) ( b ) V (d ) (e) none of these 3. Let A and B be two events with P(A) = 0.25, P(B) = 0.45, and P(An B) = 0.10. The probability P(An B) is equal to (a) 0.25 (b) 0.30 V(c) 0.35 (d) 0.40 (e) 0.45 4. Let A and B be two events with P(A) = 0.4, P(B) = 0.3 and P(A U B) = 0.42. Then events A and B are (a) independent and mutually exclusive. V(b) independent and not mutually exclusive. (c) d) not independent and mutually exclusive. not independent and not mutually exclusive. none of the above Solution: P(A U B) = 1 - 0.42 = 0.58. Then P(A) + P(B) - P(An B) = 0.58, 0.4 + 0.3 - P(An B) = 0.58, P(An B) = 0.4 + 0.3 - 0.58 = 0.12 = P(A)P(B), so A and B are independent. 5. A firm has 500 employees: 350 of them are university graduates, 400 of them have attended vocational training, and 300 of them are both university graduates and have attended vocational training. If an employee is chosen at random, what is the probability that this employee is a university graduate or has attended vocational training or both? (a) 0.6 (b ) 0.7 (c) 0.8 V(d) 0.9 (e) none of these 6. Two events A and B be two events such that P(A) = 0.2, P(B)=0.3 and P(A B) = 0.4. Let A be the complement of A. The probability P(AG|B ) is equal to (a ) W/ I ( b ) + 1 V ( d ) W/ N (e) none of these7. Let A and B be two events such that P(A) = 0.4, P(B)=0.5 and P(Ar B) =0.1. What is the probability that A or B but not both occur? (a) 0.1 (b) 0.3 (c) 0.5 V (d) 0.7 (e) 0.9 8. Suppose five good fuses and two defective fuses have been mixed up. To find the defective fuses, we test them one-by-one, at random and without replacement. The probability that both defective fuses are found in the first two tests is V(a) 21 ( b ) = (c)= (d) (e) none of these Questions 9-11. A sample of 5 observations is given: 10, 15, 30, 30, 40. 9. The mode is closest to (a) 15 (b) 20 (c) 25 (d) 30 (e) 35 10. The median is closest to (a) 15 (b) 20 (c) 25 V(d) 30 (e) 35 11. The standard deviation is closest to (a) 10.95 V(b) 12.25 (c) 120 (d) 150 (e) 170 Questions 12-13. A test is given to a sample of 100 students. Suppose the mean and standard deviation of the test scores are 40 and 10, respectively. The instructor increases each test score by 10%, and then adds 5 marks to each score after the 10% increase. As the result of these changes. 12. the new mean is closest to (a) 45 V(b) 49 (c) 53 (d) 57 (e) 61 13. the new standard deviation is closest to (a) 9 (b) 10 V(c) 11 (d) 13 (e) 15