probability

Analytical Methods for Business (University of Arizona)

ch06

Student:

1. A consistent accidental wavering is characterized by uncounconsideration appraises and can prosper on any appraise among an moderationtime.

True False

2. We are frequently zealous in decision the likelihood that a consistent accidental wavering assumes a detail appraise.

True False

3. The likelihood shortsightedness part of a consistent accidental wavering can be present as a match of the likelihood magnitude part of a discrete accidental wavering.

True False

4. Cumulative arrangement parts can solely be used to admire probabilities for consistent accidental waverings.

True False

5. The consistent unvarying arrangement represents a accidental wavering, defined on the moderationdate [a, b], that has an correspondently slight hazard of bombastic appraises among any submeandate of [a, b] delay the selfselfidentical prolixity.

True False

6. The likelihood shortsightedness part of a consistent unvarying arrangement is unequivocal for all appraises among - and +.

True False

7. The moderation of a consistent unvarying arrangement is barely the balance of the remarkable and inferior limits of the moderationdate on which the arrangement is defined.

True False

8. The moderation and exemplar sinuosity of the consistent unvarying arrangement are correspondent. Penny False

9. The likelihood shortsightedness part of a natural arrangement is in unconcealed characterized by entity symmetric and bell-shaped.

True False

10. Examples of accidental waverings that air-tight prosper a natural arrangement inferiorstand the age and the adjust year appointment of a school novice.

True False

11. Consecrated that the likelihood arrangement is natural, it is largely vivid by its moderation μ > 0 and its exemplar sinuosity σ > 0.

True False

12. Just as in the fact of the consistent unvarying arrangement, the likelihood shortsightedness part of the natural arrangement may be abundantly used to admire probabilities.

True False

13. The exemplar natural arrangement is a natural arrangement delay a moderation correspondent to cipher and a exemplar sinuosity correspondent to one.

True False

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14. The epistle Z is used to state a accidental wavering delay any natural arrangement. Penny False

15. The exemplar natural consideration is besides referred to as the z consideration. Penny False

16. Which of the prospering is emend?

A. A consistent accidental wavering has a likelihood shortsightedness part but not a cumulative arrangement part.

B. A discrete accidental wavering has a likelihood magnitude part but not a cumulative arrangement part. C.A consistent accidental wavering has a likelihood magnitude part, and a discrete accidental wavering has a

likelihood shortsightedness part.

D.A consistent accidental wavering has a likelihood shortsightedness part, and a discrete accidental wavering has a likelihood magnitude part.

17. Which of the prospering does not portray a consistent accidental wavering?

A. Climax of oak trees in a close.

B. Heights and weights of newborn babies.

C. Date of a escape among Chicago and New York.

D. The number of customer arrivals to a bank among 10 am and 11 am.

18. Which of the prospering is not a individuality of a likelihood shortsightedness part f(x)?

A. f(x) 0 for all appraises of x.

B. f(x) is symmetric encircling the moderation.

C. The area inferior f(x) balance all appraises of x correspondents one.

D. f(x) beseems cipher or approaches cipher if x increases to +instantaneousness or decreases to -infinity.

19. The cumulative arrangement part is stated and defined as which of the prospering?

A. f(x) and f(x) = P(X x)

B. f(x) and f(x) = P(X x )

C. F(x) and F(x) = P(X x)

D. F(x) and F(x) = P(X x)

20. The cumulative arrangement part F(x) of a consistent accidental wavering X delay the likelihood shortsightedness part f(x) is which of the prospering?

A. The area inferior f balance all appraises x

B. The area inferior f balance all appraises that are x or short

C. The area inferior f balance all appraises that are x or further

D. The area inferior f balance all non-privative appraises that are x or short

21. A consistent accidental wavering has the unvarying arrangement on the moderationdate [a, b] if its likelihood shortsightedness

part f(x) .

A. Is symmetric encircling its moderation

B. Is bell-shaped among a and b

C. Is fixed for all x among a and b, and 0 otherwise

D. Asymptotically approaches the x axis when x increases to + or decreases to -

22. The climax of the likelihood shortsightedness part f(x) of the unvarying arrangement defined on the moderationdate [a, b]

is .

A. 1/(b - a) among a and b, and cipher otherwise

B. (b - a)/2 among a and b, and cipher otherwise

C. (a + b)/2 among a and b, and cipher otherwise

D. 1/(a + b) among a and b, and cipher otherwise

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23. The doubt date at an elevator is unvaryingly reserved among 30 and 200 relieves. Discover the moderation and exemplar sinuosity of the doubt date.

A. 115 relieves and 49.07 relieves

B. 1.15 tinys and 0.4907 tinys

C. 1.15 tinys and 24.08333 (minute)2

D. 115 relieves and 2408.3333 (second)2

24. The doubt date at an elevator is unvaryingly reserved among 30 and 200 relieves. What is the likelihood a rider must abide among 1 tiny and 1.5 tinys?

A. 0.1765

B. 0.3529

C. 0.5294

D. 0.8824

25. The doubt date at an elevator is unvaryingly reserved among 30 and 200 relieves. What is the likelihood a rider must abide further than 1.5 tinys?

A. 0.3529

B. 0.4500

C. 0.5294

D. 0.6471

26. The doubt date at an elevator is unvaryingly reserved among 30 and 200 relieves. What is the likelihood a rider abides short than two tinys?

A. 0.4706

B. 0.5294

C. 0.6000

D. 0.7059

27. The date of a allure to a technical food cord is unvaryingly reserved among 2 and 10 tinys. What are the moderation and hostility of this arrangement?

A. 6 tinys and 2.3094 (minutes)2

B. 6 tinys and 5.3333 (minutes)2

C. 6 tinys and 5.3333 tinys

D. 8 tinys and 2.3094 tinys

28. An analyst is speculation net allowance for Excellence Corporation for the contiguous fiscal year. Her low-end admire of net allowance is $250,000, and her high-end admire is $350,000. Prior lore allows her to

assume that net allowance prospers a consistent unvarying arrangement. The likelihood that net allowance conciliate be

main than or correspondent to $337,500 is .

A. 12.5%

B. 29.6%

C. 87.5%

D. 96.4%

29. Alex is in a press to get to exertion and is dashing to seize the bus. She recognizes that the bus arrives full six tinys during dash hour, but does not recognize the straight dates the bus is due. She realizes that from the date she arrives at the seal, the whole of date that she conciliate possess to abide prospers a unvarying arrangement delay a inferior frisk of 0 tinys and an remarkable frisk of six tinys. What is the likelihood that she conciliate possess to abide further than two tinys?

A. 0.1667

B. 0.3333

C. 0.6667

D. 1.0000

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30. Suppose the balance worth of gasocord for a city in the United States prospers a consistent unvarying arrangement delay a inferior frisk of $3.50 per gallon and an remarkable frisk of $3.80 per gallon. What is the likelihood a accidentally clarified gas occupation reckoning further than $3.70 per gallon?

A. 0.3000

B. 0.3333

C. 0.6667

D. 1.0000

31. How sundry parameters are demanded to largely represent any natural arrangement?

A. 1

B. 2

C. 3

D. 4

32. What does it moderation when we say that the tails of the natural deflexion are asymptotic to the x axis?

A. The tails get closer and closer to the x axis but never move it.

B. The tails gets closer and closer to the x axis and however move it.

C. The tails get closer and closer to the x axis and however peevish this axis.

D. The tails get closer and closer to the x axis and however beseem this axis.

33. The likelihood that a natural accidental wavering is short than its moderation is .

A. 0.0

B. 0.5

C. 1.0

D. Cannot be determined

34. Let X be naturally reserved delay moderation μ and exemplar sinuosity σ > 0. Which of the prospering is penny about the z appraise identical to a consecrated x appraise?

A. A unequivocal z = (x - μ)/σ indicates how sundry exemplar sinuositys x is overhead μ.

B. A privative z = (x - μ)/σ indicates how sundry exemplar sinuositys x is inferior μ.

C. The z appraise identical to x = μ is cipher.

D. All of the overhead.

35. It is recognizen that the prolixity of a undoubtful result X is naturally reserved delay μ = 20 inches. How is the

likelihood kindred to ?

A. is main than .

B. is smaller than .

C. is the selfselfidentical as .

D. No similarity can be made delay the consecrated counsel.

36. It is recognizen that the prolixity of a undoubtful result X is naturally reserved delay μ = 20 inches. How is the

likelihood kindred to ?

A. is main than .

B. is smaller than .

C. is the selfselfidentical as .

D. No similarity can be made delay the consecrated counsel.

37. It is recognizen that the prolixity of a undoubtful result X is naturally reserved delay μ = 20 inches. How is the

likelihood kindred to ?

A. is main than .

B. is smaller than .

C. is the selfselfidentical as .

D. No similarity can be made delay the consecrated counsel.

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38. It is recognizen that the prolixity of a undoubtful result X is naturally reserved delay μ = 20 inches and σ = 4

inches. How is the likelihood kindred to ?

A. is main than .

B. is smaller than .

C. is the selfselfidentical as .

D. No similarity can be made delay the consecrated counsel.

39. The likelihood P(Z < -1.28) is closest to .

A. -0.10

B. 0.10

C. 0.20

D. 0.90

40. The likelihood P(Z > 1.28) is closest to .

A. -0.10

B. 0.10

C. 0.20

D. 0.90

41. Discover the likelihood P(-1.96 Z 0).

A. 0.0250

B. 0.0500

C. 0.4750

D. 0.5250

42. Discover the likelihood P(-1.96 Z 1.96).

A. 0.0500

B. 0.9500

C. 0.9750

D. 1.9500

43. Discover the z appraise such that .

A. z = -1.33

B. z = 0.1814

C. z = 0.8186

D. z = 1.33

44. Discover the z appraise such that .

A. z = -1.645

B. z = -1.96

C. z = 1.645

D. z = 1.96

45. You exertion in marketing for a assembly that produces exertion boots. Quality coerce has sent you a memo detailing the prolixity of date anteriorly the boots waste out inferior impenetrable use. They discover that the boots waste out in an balance of 208 days, but the straight whole of date varies, prospering a natural arrangement delay a exemplar sinuosity of 14 days. For an upcoming ad belligerence, you demand to recognize the percent of the pairs that definite longer than six monthsthat is, 180 days. Use the experimental government to approach this percent.

A. 2.5%

B. 5%

C. 95%

D. 97.5%

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