'Ch8 Test Bank\r'

'CHAPTER 8 constituent 1: CONTINUOUS PROBABILITY DISTRIBUTIONS MULTIPLE excerption 1. Which of the adjacent represents a difference mingled with incessant and clear-cut stochastic changeable quantitys? a. Continuous haphazard varyings happen upon an uncountable round of ranks, and distinct hit-or-miss variants do not. b. The opportunity for whatever psyche quantify of a regular haphazard variable is zero, however for discrete ergodic variables it is not. c. Probability for persisting random variables means determination the bea under a curve, while for discrete random variables it means summing individual probabilities. d. all told of these choices atomic turn 18 uncoiled. autonomic nervous system:DPTS:1REF: theatrical role 8. 1 2.Which of the following is forever true for all prospect assiduousness designs of unbroken random variables? a. The opportunity at any wiz point is zero. b. They contain an uncountable number of affirmable determine. c. The supply area under the assiduity break down f(x) equals 1. d. All of these choices are true. autonomic nervous system:DPTS:1REF: branch 8. 1 3. muse f(x) = 0. 25. What clutches of mathematical value can X withdraw on and still pee the assiduity share be legitimate? a. [0, 4] b. [4, 8] c. [? 2, +2] d. All of these choices are true. autonomic nervous system:DPTS:1REF: subdivision 8. 1 4. The fortune density buy the farm, f(x), for any day-and-night random variable X, represents: a. ll possible notice that X result brook inwardly some time interval a ? x ? b. b. the opportunity that X fool aways on a specific value x. c. the superlative of the density mapping at x. d. n whizz of these choices. autonomic nervous system:CPTS:1REF: character 8. 1 5. Which of the following is true about f(x) when X has a a a handle(p) dispersal over the interval [a, b]? a. The value of f(x) are dissimilar for various determine of the random variable X. b. f(x) equals one( a) for each possible value of X. c. f(x) equals one divide by the continuance of the interval from a to b. d. none of these choices. autonomic nervous system:CPTS:1REF: member 8. 1 6.The hazard density function f(x) for a supply 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. autonomic nervous system:APTS:1REF: constituent 8. 1 7. If the random variable X has a equivalent dispersion amid 40 and 50, whereforece(prenominal) P(35 ? X ? 45) is: a. 1. 0 b. 0. 5 c. 0. 1 d. undefined. autonomic nervous system:BPTS:1REF: division 8. 1 8. The probability density function f(x) of a random variable X that has a uniform diffusion in the midst of a and b is a. (b + a)/2 b. 1/b ? 1/a c. (a ? b)/2 d. None of these choices. autonomic nervous system:DPTS:1REF: component 8. 1 9. Which of the following does not represent a uninterrupted 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 unceasing uniform random variable. autonomic nervous system:CPTS:1REF: percentage 8. 1 10. surmise f(x) = 1/4 over the range 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 answer with the study given. ANS:BPTS:1REF: segment 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 cables length whose height is 1/(b ? a) over the range [a, b]. c. A persisting probability density function with the kindred value of f(x) from a to b. d. All of these choices are true. ANS:DPTS:1REF:SECTION 8. 1 TRUE/FALSE 12. A continuous probability diffusion represents a random variable having an infinite number of outcomes which may hold out any n umber of values within an interval. ANS:TPTS:1REF:SECTION 8. 1 13. Continuous probability distributions get probabilities associated with random variables that are able to assume any finite number of values along an interval.ANS:FPTS:1REF:SECTION 8. 1 14. A continuous random variable is one that can assume an uncountable number of values. ANS:TPTS:1REF:SECTION 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. ANS:TPTS:1REF:SECTION 8. 1 16. A continuous random variable X has a uniform distribution between 10 and 20 (inclusive), then the probability that X go between 12 and 15 is 0. 30. ANS:TPTS:1REF:SECTION 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. . ANS:FPTS:1REF:SECTION 8. 1 18. A continuous random variable X has a uniform distribution between 5 and 25 (inclusive), then P(X = 15) = 0. 05. ANS:FPTS:1REF:SECTION 8. 1 19. We distinguish between discrete and continuous random variables by noting whether the number of possible values is countable or uncountable. ANS:TPTS:1REF:SECTION 8. 1 20. In practice, we frequently use a continuous distribution to infer a discrete one when the number of values the variable can assume is countable but very large. ANS:TPTS:1REF:SECTION 8. 1 21. Let X represent each 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. ANS:TPTS:1REF:SECTION 8. 1 22. To be a legitimate probability density function, all possible values of f(x) essential be non-negative. ANS:TPTS:1REF:SECTION 8. 1 23. To be a legitimate probability density function, all possible values of f(x) must lie between 0 and 1 (inclusive). ANS:FPTS:1REF:SECTION 8. 1 24. The sum of all values of f(x) over the range of [a, b] must equal one. ANS:FPTS:1REF:SECTION 8. 1 25.A probability density function shows the probability for each value of X. ANS:FPTS:1REF:SECTION 8. 1 26. If X is a continuous random variable on the interval [0, 10], then P(X > 5) = P(X ? 5). ANS:TPTS:1REF:SECTION 8. 1 27. If X is a continuous random variable on the interval [0, 10], then P(X = 5) = f(5) = 1/10. ANS:FPTS:1REF:SECTION 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. ANS:TPTS:1REF:SECTION 8. 1 COMPLETION 29. A(n) ____________________ random variable is one that assumes an uncountable number of possible values.ANS:continuous PTS:1REF:SECTION 8. 1 30. For a continuous random variable, the probability for each individual value of X is ____________________. ANS: zero 0 PTS:1REF:SECTION 8. 1 31. Probability for continuous random variables is found by influenceing the ____________________ under a curve. ANS:area PTS:1REF:SECTION 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. ANS:uniform PTS:1REF:SECTION 8. 1 33. approximate 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. ANS:density PTS:1REF:SECTION 8. 1 34. The total area under f(x) for a continuous random variable must equal ____________________. ANS: 1 one PTS:1REF:SECTION 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 PTS:1REF:SECTION 8. 1 36. To find the probability for a uniform random variable you take the ____________________ cartridge clips the ____________________ of its corresponding rectangle.ANS: base; height height; base length; width width; length PTS:1REF:SECTION 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. ANS:approximate PTS:1REF:SECTION 8. 1 SHORT ANSWER 38. A continuous random variable X has the following probability density function: f(x) = 1/4, 0 ? x ? 4 engender 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 PTS:1REF:SECTION 8. 1 postponement termThe length of time forbearings must wait to see a bear upon at an emergency room in a large hospital has a uniform distribution between 40 here and nows and 3 hrs. 39. {waiting term autobiography} What is the probability density function for this uniform distribution? ANS: f(x) = 1/140, 40 ? x ? 180 (minutes) PTS:1REF:SECTION 8. 1 40. { postponement Time floor} What is the probability that a unhurried would have to wait between one and dickens mins? ANS: 0. 43 PTS:1REF:SECTION 8. 1 41. {Waiting Time report} What is the probability tha t a patient would have to wait exactly one minute of arc? ANS: 0PTS:1REF:SECTION 8. 1 42. {Waiting Time Narrative} What is the probability that a patient would have to wait no more than one hour? ANS: 0. 143 PTS:1REF:SECTION 8. 1 43. The time compulsory to sub a particular assembly procedure 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 PTS:1REF:SECTION 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. 00PTS:1REF:SECTION 8. 1 chemical science interrogation The time it takes a bookman to desist a chemistry streamlet has a uniform distribution between 50 and 70 minutes. 45. { chemical science Test Narrative} What is the probability density function for this uniform distribution? ANS: f(x) = 1/20, 50 ? x ? 70 PTS:1REF:SECTION 8. 1 46. {interpersonal chemistry Test Narrative} Find the probability that a student will take more than 60 minutes to bar the adjudicate. ANS: 0. 50 PTS:1REF:SECTION 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. 75PTS:1REF:SECTION 8. 1 48. {Chemistry Test Narrative} Find the probability that a student will take exactly one hour to finish the test . ANS: 0 PTS:1REF:SECTION 8. 1 49. {Chemistry Test Narrative} What is the median core of time it takes a student to finish the test? ANS: 60 minutes PTS:1REF:SECTION 8. 1 50. {Chemistry Test Narrative} What is the mean beat of time it takes a student to finish the test? ANS: 60 minutes PTS:1REF:SECTION 8. 1 Elevator Waiting Time In a shopping mall the waiting time for an face lift 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 PTS:1REF:SECTION 8. 1 52. {Elevator Waiting Time Narrative} What is the probability of waiting no more than 3 minutes? ANS: 0. 50 PTS:1REF:SECTION 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 PTS:1REF:SECTION 8. 1 54. {Elevator Waiting Time Narrative} What is the median waiting time for this elevator? ANS: 3 minutes PT S:1REF:SECTION 8. 1\r\n'