Module 8 Review Questions

Module 8 Review Questions Answer the following multiple choice questions: 1. In a large population of college students, 20% of the students have experienced feelings of math anxiety. If you take a random sample of 10 students from this population, the probability that exactly 2 students have experienced math anxiety is (a) 0.3020 (b) 0.2634 (c) 0.2013 (d) 0.5 (e) 1 (f) None of the above 2. Refer to the previous problem. The standard deviation of the number of students in the sample who have experienced math anxiety is (a) 0.0160 (b) 1.265 (c) 0.2530 (d) 1 (e) .2070 3. In a certain large population, 40% of households have a total annual income of $70,000 (or more). A simple random sample of 4 of these households is selected. What is the probability that 2 or more of the households in the survey have an annual income of over $70,000? (a) 0.3456 (b) 0.4000 (c) 0.5000 (d) 0.5248 (e) The answer cannot be computed from the information given. 4. Refer to the previous problem. What is the probability that between 1 and 3 (inclusive) households in the survey have an annual income of over $70,000? (a) 0.1552 (b) 0.3456 (c) 0.4992 (d) 0.8448 (e) The answer cannot be computed from the information given. 5. A factory makes silicon chips for use in computers. It is known that about 90% of the chips meets specifications. Every hour a sample of 18 chips is selected at random for testing. Assume a binomial distribution is valid. Suppose we collect a large number of these samples of 18 chips and determine the number meeting specifications in each sample. What is the approximate mean of the number of chips meeting specifications? (a) 16.20 (b) 1.62 (c) 4.02 (d) 16.00 (e) The answer cannot be computed from the information given. 6. Which of the following are true statements? I. The expected value of a geometric random variable is determined by the formula (1 – p)n–1p. II. If X is a geometric random variable and the probability of success is .85, then the probability distribution of X will be skewed left, since 85 is closer to 1 than to 0. III. An important difference between binomial and geometric random variables is that there is a fixed number of trials in a binomial setting, and the number of trials varies in a geometric setting. (a) I only (b) II only (c) III only (d) I, II, and III (e) None of the above gives the complete set of true responses. 7. A fair coin (one for which both the probability of heads and the probability of tails are 0.5) is tossed six times. Use the binomial formula to evaluate the probability that less than 1/3 of the tosses are heads is (a) 0.344. (b) 0.33. (c) 0.109. (d) 0.09. (e) 0.0043. 8. A college basketball player makes 80% of his free throws. At the end of a game, his team is losing by two points. He is fouled attempting a three-point shot and is awarded three free throws. Assuming each free throw is independent, what is the probability that he makes at least two of the free throws? (a) 0.896. (b) 0.80. (c) 0.512. (d) 0.384. (e) 0.20. 9. It has been estimated that about 30% of frozen chickens contain enough salmonella bacteria to cause illness if improperly cooked. A consumer purchases 12 frozen chickens. What is the probability that the consumer will have more than 6 contaminated chickens? (a) 0.961 (b) 0.118 (c) 0.882 (d) 0.039 (e) 0.079 10. 30% of all New Yorkers are immigrants. If you meet randomly selected New Yorkers, what is the probability that the first immigrant you meet is the third person you meet? (a) .0333 (b) .147 (c) .3000 (d) .853 (e) None of the above gives the complete set of true responses. Answers: 1. a 2. b 3. d 4. d 5. a 6. c 7. c 8. a 9. d 10. b