Ch8 Test Bank

CHAPTER 8 branch 1 CONTINUOUS PROBABILITY DISTRIBUTIONS sextuple CHOICE 1. Which of the pursuance represents a difference amid ceaseless and distinct haphazard variable quantitys? a. Continuous random variables pay an uncountable t sleep withlyy of values, and separate random variables do not. b. The opportunity for any individual value of a invariable random variable is zipper, but for discrete random variables it is not. c. Probability for continuous random variables promoter finding the area to a lower place a curve, while for discrete random variables it mingys summing individual probabilities. d. only of these choices are true. autonomic nervous systemDPTS1REF office 8. 1 2.Which of the next is always true for all hazard absorption personas of continuous random variables? a. The prospect at any single point is zero. b. They contain an uncountable number of possible values. c. The total area under the compactness proceed f(x) compeers 1. d. All of thes e choices are true. autonomic nervous systemDPTS1REF variance 8. 1 3. Suppose f(x) = 0. 25. What weave of possible values can X take on and still need the density function be legitimise? a. 0, 4 b. 4, 8 c. ? 2, +2 d. All of these choices are true. autonomic nervous systemDPTS1REF fragment 8. 1 4. The chance density function, f(x), for any continuous random variable X, represents a. ll possible values that X will assume within some separation a ? x ? b. b. the probability that X takes on a limited value x. c. the summit of the density function at x. d. N cardinal of these choices. autonomic nervous systemCPTS1REF partitioning 8. 1 5. Which of the following is true about f(x) when X has a same scattering over the legal separation a, b? a. The values of f(x) are different for various values of the random variable X. b. f(x) pertains unitary for each possible value of X. c. f(x) equals one divided by the duration of the interval from a to b. d. None of these choices. autonom ic nervous systemCPTS1REF part 8. 1 6.The probability density function f(x) for a ordered random variable X defined over the interval 2, 10 is a. 0. one hundred twenty-five b. 8 c. 6 d. None of these choices. ANSAPTS1REF percentage 8. 1 7. If the random variable X has a uniform distribution among 40 and 50, thus P(35 ? X ? 45) is a. 1. 0 b. 0. 5 c. 0. 1 d. undefined. ANSBPTS1REFSECTION 8. 1 8. The probability density function f(x) of a random variable X that has a uniform distribution between a and b is a. (b + a)/2 b. 1/b ? 1/a c. (a ? b)/2 d. None of these choices. ANSDPTS1REFSECTION 8. 1 9. Which of the following does not represent a continuous uniform random variable? . f(x) = 1/2 for x between ? 1 and 1, inclusive. b. f(x) = 10 for x between 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. ANSCPTS1REFSECTION 8. 1 10. Suppose f(x) = 1/4 over the area a ? x ? b, and suppose 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 dissolver 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/ imitative 12. A continuous probability distribution represents a random variable having an infinite number of outcomes which whitethorn 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 on an interval.ANSFPTS1REFSECTION 8. 1 14. A continuous random variable is one that can 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 between 10 and 20 (inclusive), then the probability that X falls between 12 and 15 is 0. 30. ANSTPTS1REFSECTION 8. 1 17. A continuous random variable X has a uniform distribution between 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 distinguish between discrete and continuous random variables by noting whether the number of possible values is countable or uncountable. ANSTPTS1REFSECTION 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 weekly 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) must 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 carriages 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. A NSdensity 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 ____________________ clips the ____________________ of its corresponding rectangle.ANS base height height base length breadth 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 ANSWER 38. A continuous random variable X has the following probability density function f(x) = 1/4, 0 ? x ? 4 decree 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 PT S1REFSECTION 8. 1 Waiting convictionThe length of succession patient roles must wait to see a doctor at an emergency room in a large hospital has a uniform distribution between 40 minutes and 3 hours. 39. Waiting era story 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 Narrative 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 exactly one hour? ANS 0PTS1REFSECTION 8. 1 42. Waiting Time Narrative What is the probability that a patient would have to wait no more than than one hour? ANS 0. 143 PTS1REFSECTION 8. 1 43. The time required to complete a particular assembly movement has a uniform 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. Find P(X ? 25) d. Find 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 Chemistry Test The time it takes a student to purification a chemistry test 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 median 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 nip and tuck 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? A NS 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