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Probability and statistics (0936251) Student name:----------------------------Student number:--------------------------- First exam October, 31, 2013 Section:---------------------------------- Select the best answer for each of the following questions, and fill your answers in the table below question 1 2 3 4 5 6 7 8 9 10 solution question 11 12 13 14 15 16 17 18 19 20 Good luck solution 1. If two events (both with probability greater than 0) are mutually exclusive, then: A. They also must be complements. B. They also could be complements. C. They cannot be complements. 2. An artist has 9 paintings. How many ways can he hang 4 paintings side-by-side on a gallery wall? A. B. C. D. 9! 9! 5! 9! 4! 9 ( ) 4 3. Which one of these variables is a continuous random variable? A. B. C. D. The time it takes a randomly selected student to complete an exam. The number of times a randomly selected student repeat a course. The number of women taller than 68 inches in a random sample of 5 women. The number of correct guesses on a multiple choice test. 4. Suppose we toss a fair coin 8 times. What is the probability that the sequence of 8 tosses yields 3 heads (H) and 5 tails (T)? A. B. C. D. E. 0.003906 0.017857 0.21875 0.125 None of the above 5. A medical treatment has a success probability of 0.8. Two patients will be treated with this treatment. Assuming the results are independent for the two patients, what is the probability that no one of them will be successfully treated? A. B. C. D. 0.04 0 .5 0.36 0.2 6. A particular company has twenty salespeople. In how many ways can a group of three salespeople be selected from this company? A. 8000 B. 6840 C. 5700 D. 1140 E. 2210 7. Which of the following is not true concerning discrete probability distribution? A. The probability of any specific value is between 0 and 1, inclusive. B. The mean of the distribution is between the smallest and largest value of the discrete random variable. C. The sum of all probabilities is 1. D. The standard deviation of the distribution is between -1 and 1. Use the information below to answer questions (8- 9) A business evaluates a proposed project as follows. It stands to make a profit of $10,000 with probability 0.15 , to make profit of $5,000 with probability 0.45 , to break even with probability 0.25 and to loose $5,000 with probability 0.15 . Profit Profit Break even Loose X (profit) 10,000 5,000 0 -5,000 P(X) probability 0.15 0.45 0.25 0.15 8. The expected profit in dollars is: A. B. C. D. E. 1,500 0 -1,500 3,250 3,000 9. The standard deviation for profit in dollars is A. B. C. D. E. 4582.6 √21000 21000000 5477.2 None of the above Use the information below to answer questions ( 10-13 ) In a market study, a researcher found that 30% of customers are repeat customers. If 10 customers are selected at random. 10. Find the probability that at least one customer is repeat customer. A. B. C. D. E. 0.02825 0.149308 0.97175 0.850692 None of the above 11. find the probability that exactly 7 are repeat customers. A. B. C. D. E. 0.991 0.009 0.2668 0.733 None of the above 12. How many would you expect to be repeat customers? A. B. C. D. E. 3 0.3 7 5 None of the above 13. The standard deviation for the number of repeat customers is ? A. B. C. D. E. √30 1.449 210 5 None of the above 14. If X is a binomial random variable with parameters (n=20) and (p=0.2). The cumulative distribution function for the random variable X is A. B. C. D. E. Defined only for the integer numbers (0, 1, 2, 3 , …….,20). Defined Only on the interval 0 ≤ 𝑥 ≤ 20 Defined on any real number greater than or equal to zero. Defined on any real number on the interval (−∞ ≤ 𝑥 ≤ ∞) Equal to 0.00203 at (X =10 ) Use the information below to answer questions (15-18 ) Given the following cumulative distribution function for the random variable X: 0 𝑥<2 0.25 2≤𝑥<4 0.5 4≤𝑥<6 𝐹(𝑥) = 0.75 6≤𝑥<8 1 8≤𝑥 { 𝑃(6 ≤ 𝑥 ≤ 8) = 15. A. B. C. D. E. Zero 0.25 0.5 0.75 None of the above 𝑃(𝑥 > 7) = 16. A. B. C. D. E. 17. Zero 0.25 0.75 1 None of the above 𝑃(𝑥 = 9) = A. B. C. D. E. Zero 0.25 0.75 1 None of the above 18. The random variable X is A. B. C. D. A binomial random variable A discrete uniform random variable A continuous random variable Defined for any real number on the interval (−∞ ≤ 𝑥 ≤ 10) Use the information below to answer questions ( 19-20 ) Three machines A, B and C produce 20%, 45% and 35% respectively of a factory's wheel nuts output. 2%, 1% and 3% respectively of these machines outputs are defective. 19. What is the probability that any wheel nut randomly selected from the factory's stock will be defective? A. B. C. D. E. 0.06 0.004 0.019 0.6 None of the above 20. What is the probability that a randomly selected wheel nut comes from machine A if it is not defective? A. B. C. D. E. 0.004077 0.799185 0.200815 0.199796 None of the above