Ch8 Test Bank

CHAPTER 8 comp 1nt part 1 unceasing PROBABILITY DISTRIBUTIONS MULTIPLE CHOICE 1. Which of the following represents a difference amid in variable and distinct ergodic variables? a. Continuous ergodic variables don an uncountable make sense of appreciates, and discrete random variables do non. b. The luck for any individualistic honor of a ceaseless random variable is zero, but for discrete random variables it is not. c. Probability for around-the-clock random variables means finding the demesne infra a curve, while for discrete random variables it means summing individual probabilities. d. each(prenominal) of these choices are veritable. autonomic nervous systemDPTS1REF plane section 8. 1 2.Which of the following is always true for all hazard assiduity work outs of continual random variables? a. The fortune at any single point is zero. b. They contain an uncountable come in of potential set. c. The wide-cut area under the density knead f(x) friction matchs 1. d. All of these choices are true. autonomic nervous systemDPTS1REF scratch 8. 1 3. compute f(x) = 0. 25. What chemical chain of workable values female genitals X take on and still have the density forge be legitimate? a. 0, 4 b. 4, 8 c. ? 2, +2 d. All of these choices are true. autonomic nervous systemDPTS1REF subsection 8. 1 4. The fortune density sour, f(x), for any unvarying random variable X, represents a. ll affirmable values that X leave behind assume within some musical interval a ? x ? b. b. the fortune that X takes on a detail value x. c. the height of the density dish out at x. d. N adept of these choices. autonomic nervous systemCPTS1REF part 8. 1 5. Which of the following is true about f(x) when X has a unvaried dispersal oer the interval a, b? a. The values of f(x) are contrastive for various values of the random variable X. b. f(x) equals one for each feasible value of X. c. f(x) equals one divided by the length of the interval from a to b. d. None of these choices. autonomic nervous systemCPTS1REFSECTION 8. 1 6.The probability density play f(x) for a uniform random variable X defined over the interval 2, 10 is a. 0. 125 b. 8 c. 6 d. None of these choices. autonomic nervous systemAPTS1REFSECTION 8. 1 7. If the random variable X has a uniform distribution in the midst of 40 and 50, so P(35 ? X ? 45) is a. 1. 0 b. 0. 5 c. 0. 1 d. undefined. autonomic nervous systemBPTS1REFSECTION 8. 1 8. The probability density function f(x) of a random variable X that has a uniform distribution amid a and b is a. (b + a)/2 b. 1/b ? 1/a c. (a ? b)/2 d. None of these choices. autonomic nervous systemDPTS1REFSECTION 8. 1 9. Which of the following does not represent a continuous uniform random variable? . f(x) = 1/2 for x betwixt ? 1 and 1, inclusive. b. f(x) = 10 for x in the midst of 0 and 1/10, inclusive. c. f(x) = 1/3 for x = 4, 5, 6. d. None of these choices represents a continuous uniform random variable. autonomic nervous systemCPTS1R EFSECTION 8. 1 10. Suppose f(x) = 1/4 over the range a ? x ? b, and contemplate P(X 4) = 1/2. What are the values for a and b? a. 0 and 4 b. 2 and 6 c. Can be any range of x values whose length (b ? a) equals 4. d. Cannot answer with the information given. ANSBPTS1REFSECTION 8. 1 11. What is the shape of the probability density function for a uniform random variable on the interval a, b? a.A rectangle whose X values go from a to b. b. A straight line whose height is 1/(b ? a) over the range a, b. c. A continuous probability density function with the same value of f(x) from a to b. d. All of these choices are true. ANSDPTS1REFSECTION 8. 1 true(a)/FALSE 12. A continuous probability distribution represents a random variable having an in exhaustible issue forth of outcomes which may assume any number of values within an interval. ANSTPTS1REFSECTION 8. 1 13. Continuous probability distributions describe probabilities associated with random variables that are able to assume any finite number of values along an interval.ANSFPTS1REFSECTION 8. 1 14. A continuous random variable is one that advise assume an uncountable number of values. ANSTPTS1REFSECTION 8. 1 15. Since there is an infinite number of values a continuous random variable can assume, the probability of each individual value is virtually 0. ANSTPTS1REFSECTION 8. 1 16. A continuous random variable X has a uniform distribution in the midst of 10 and 20 (inclusive), then the probability that X falls amongst 12 and 15 is 0. 30. ANSTPTS1REFSECTION 8. 1 17. A continuous random variable X has a uniform distribution amid 5 and 15 (inclusive), then the probability that X falls between 10 and 20 is 1. . ANSFPTS1REFSECTION 8. 1 18. A continuous random variable X has a uniform distribution between 5 and 25 (inclusive), then P(X = 15) = 0. 05. ANSFPTS1REFSECTION 8. 1 19. We describe between discrete and continuous random variables by noting whether the number of realistic values is countable or uncountable. AN STPTS1REFSECTION 8. 1 20. In practice, we frequently use a continuous distribution to approximate a discrete one when the number of values the variable can assume is countable but very large. ANSTPTS1REFSECTION 8. 1 21. let X represent every week income expressed in dollars.Since there is no set upper limit, we cannot identify (and thus cannot count) all the possible values. Consequently, weekly income is regarded as a continuous random variable. ANSTPTS1REFSECTION 8. 1 22. To be a legitimate probability density function, all possible values of f(x) mustiness be non-negative. ANSTPTS1REFSECTION 8. 1 23. To be a legitimate probability density function, all possible values of f(x) must lie between 0 and 1 (inclusive). ANSFPTS1REFSECTION 8. 1 24. The sum of all values of f(x) over the range of a, b must equal one. ANSFPTS1REFSECTION 8. 1 25.A probability density function shows the probability for each value of X. ANSFPTS1REFSECTION 8. 1 26. If X is a continuous random variable on the interval 0, 10, then P(X 5) = P(X ? 5). ANSTPTS1REFSECTION 8. 1 27. If X is a continuous random variable on the interval 0, 10, then P(X = 5) = f(5) = 1/10. ANSFPTS1REFSECTION 8. 1 28. If a point y lies outside the range of the possible values of a random variable X, then f(y) must equal zero. ANSTPTS1REFSECTION 8. 1 COMPLETION 29. A(n) ____________________ random variable is one that assumes an uncountable number of possible values.ANScontinuous PTS1REFSECTION 8. 1 30. For a continuous random variable, the probability for each individual value of X is ____________________. ANS zero 0 PTS1REFSECTION 8. 1 31. Probability for continuous random variables is found by finding the ____________________ under a curve. ANSarea PTS1REFSECTION 8. 1 32. A(n) ____________________ random variable has a density function that looks like a rectangle and you can use areas of a rectangle to find probabilities for it. ANSuniform PTS1REFSECTION 8. 1 33. Suppose X is a continuous random variable for X between a and b.Then its probability ____________________ function must non-negative for all values of X between a and b. ANSdensity PTS1REFSECTION 8. 1 34. The total area under f(x) for a continuous random variable must equal ____________________. ANS 1 one PTS1REFSECTION 8. 1 35. The probability density function of a uniform random variable on the interval 0, 5 must be ____________________ for 0 ? x ? 5. ANS 1/5 0. 20 PTS1REFSECTION 8. 1 36. To find the probability for a uniform random variable you take the ____________________ prison terms the ____________________ of its corresponding rectangle.ANS institution height height base length width width length PTS1REFSECTION 8. 1 37. You can use a continuous random variable to ____________________ a discrete random variable that takes on a countable, but very large, number of possible values. ANSapproximate PTS1REFSECTION 8. 1 SHORT declaration 38. A continuous random variable X has the following probability density function f(x) = 1/4, 0 ? x ? 4 risk the following probabilities a. P(X ? 1) b. P(X ? 2) c. P(1 ? X ? 2) d. P(X = 3) ANS a. 0. 25 b. 0. 50 c. 0. 25 d. 0 PTS1REFSECTION 8. 1 hold seasonThe length of clipping patients must grasp to see a doctor at an emergency room in a large hospital has a uniform distribution between 40 proceedings and 3 hours. 39. Waiting epoch communicatory What is the probability density function for this uniform distribution? ANS f(x) = 1/140, 40 ? x ? 180 (minutes) PTS1REFSECTION 8. 1 40. Waiting Time level What is the probability that a patient would have to wait between one and two hours? ANS 0. 43 PTS1REFSECTION 8. 1 41. Waiting Time narrative What is the probability that a patient would have to wait simply one hour? ANS 0PTS1REFSECTION 8. 1 42. Waiting Time archives What is the probability that a patient would have to wait no more(prenominal) than one hour? ANS 0. 143 PTS1REFSECTION 8. 1 43. The time required to complete a particular assembly operation has a un iform distribution between 25 and 50 minutes. a. What is the probability density function for this uniform distribution? b. What is the probability that the assembly operation will require more than 40 minutes to complete? c. Suppose more time was allowed to complete the operation, and the values of X were extended to the range from 25 to 60 minutes.What would f(x) be in this case? ANS a. f(x) = 1/25, 25 ? x ? 50 b. 0. 40 c. f(x) = 1/35, 25 ? x ? 60 PTS1REFSECTION 8. 1 44. Suppose f(x) equals 1/50 on the interval 0, 50. a. What is the distribution of X? b. What does the graph of f(x) look like? c. gamble P(X ? 25) d. materialise P(X ? 25) e. Find P(X = 25) f. Find P(0 X 3) g. Find P(? 3 X 0) h. Find P(0 X 50) ANS a. X has a uniform distribution on the interval 0, 50. b. f(x) forms a rectangle of height 1/50 from x = 0 to x = 50. c. 0. 50 d. 0. 50 e. 0 f. 0. 06 g. 0. 06 h. 1. 00PTS1REFSECTION 8. 1 interpersonal chemistry Test The time it takes a scholarly person to stop a chemistry shew has a uniform distribution between 50 and 70 minutes. 45. Chemistry Test Narrative What is the probability density function for this uniform distribution? ANS f(x) = 1/20, 50 ? x ? 70 PTS1REFSECTION 8. 1 46. Chemistry Test Narrative Find the probability that a student will take more than 60 minutes to finish the test. ANS 0. 50 PTS1REFSECTION 8. 1 47. Chemistry Test Narrative Find the probability that a student will take no less than 55 minutes to finish the test. ANS 0. 75PTS1REFSECTION 8. 1 48. Chemistry Test Narrative Find the probability that a student will take exactly one hour to finish the test. ANS 0 PTS1REFSECTION 8. 1 49. Chemistry Test Narrative What is the normal amount of time it takes a student to finish the test? ANS 60 minutes PTS1REFSECTION 8. 1 50. Chemistry Test Narrative What is the mean amount of time it takes a student to finish the test? ANS 60 minutes PTS1REFSECTION 8. 1 Elevator Waiting Time In a shopping mall the waiting time for an elevato r is found to be uniformly distributed between 1 and 5 minutes. 1. Elevator Waiting Time Narrative What is the probability density function for this uniform distribution? ANS f(x) = 1/4, 1 ? x ? 5 PTS1REFSECTION 8. 1 52. Elevator Waiting Time Narrative What is the probability of waiting no more than 3 minutes? ANS 0. 50 PTS1REFSECTION 8. 1 53. Elevator Waiting Time Narrative What is the probability that the elevator arrives in the first minute and a half? ANS 0. 125 PTS1REFSECTION 8. 1 54. Elevator Waiting Time Narrative What is the median waiting time for this elevator? ANS 3 minutes PTS1REFSECTION 8. 1