Statistics > EXAM > Introduction to Biostatistics | Final exam | questions and answers| (All)

Introduction to Biostatistics | Final exam | questions and answers|

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1. The following graph is the dotplot of the data which gives the survival time (in weeks) after chemotherapy of 27 terminally-ill cancer patients. Find the mean (¯x) and the median (˜x). A) ¯x ... = 11.296, x˜ = 11 B) ¯x = 12.563, x˜ = 12 C) ¯x = 10.541, x˜ = 11 D) ¯x = 11.575, x˜ = 13 E) ¯x = 10.332, x˜ = 12 Solution: The mean is x¯ = 9 × 6 + 10 × 5 + 11 × 5 + 12 × 3 + 13 × 4 + 14 × 2 + 15 × 2 27 = 11.296 The median is ˜x = y14 = 11. The answer is A. 2. A chemical spill occurring in a river affected the fish downstream. It is estimated that 30% of the fish are contaminated, i.e. contain more than 1.5 mg of the chemical per kilogram of body weight. A fisherman has caught 5 fish. What is the probability that at least 2 fish are contaminated? A) 0.5282 B) 0.4718 C) 0.1631 D) 0.3601 E) 0.8369 Solution: Let X be the number of contaminated fish, in the sample of 5 fish. X has a binomial distribution with n = 5 trials and p = 0.30. 2 Downloaded by Namhyuk kim ([email protected]) lOMoARcPSD|6818537 The desired probability is: P(X ≥ 2) = 1 − P(X = 0) − P(X = 1) = 1 − (0.7)5 − 5(0.3)(0.7)4 = 1 − 0.1680 − 0.3601 = 1 − 0.5282 = 0.4718 The answer is B. 3. Let X be the number of smokers in a family composed of a husband and wife. X is a random variable which takes the values 0, 1, 2, with respective probabilities p0, p1, p2. The average number of smokers per family is 0.63. 40% of families contain at least one smoker. Find the probabilities p0, p1 and p2. A) p0 = 0.6, p1 = 0.35, p2 = 0.05 B) p0 = 0.6, p1 = 0.2, p3 = 0.2 C) p0 = 0.6, p1 = 0.17, p2 = 0.23 D) p0 = 0.4, p1 = 0.4, p3 = 0.2 E) p0 = 0, p1 = 0.31, p2 = 0.16 Solution: We know that P(X ≥ 1) = p1 + p2 = 0.4. Hence p0 = 0.6. We have: [Show More]

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