# Explain how random events behave in the short run and in the long run

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Review and Experience Exam Questions for Exam 2

Learning Objectives:

Chapter 17: Thinking environing luck

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Explain how haphazard smoothts bepossess in the soon run and in the crave run and how haphazard and

haphazard are not the corresponding man.

Perform basic affectlihood calculations using die flattens and fabricate tosses.

Define affectlihood, and engage the rules for affectlihood.

Explain whether the law of mediums is gentleman.

Explain how specific affectlihood differs from a philosophical or tentative affectlihood.

Chapter 18: Likelihood copys

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Define a affectlihood copy. Form a affectlihood copy for a feature anecdote’s smoothts.

Apply the basic rules of affectlihood to a anecdote example.

Calculate probabilities using a affectlihood copy, including summing up probabilities or

subtracting probabilities from the aggregate.

Define a sampling division.

Chapter 20: The scion edge: expected rates

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Define expected rate, and rate the expected rate when attached a affectlihood copy.

Define the law of liberal aggregate, and illustrate how it is divergent from the fabulous “law of

averages.”

Explain how casinos and prophylactic companies cling in office and construct specie.

Chapter 13: The Normal division

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Identify axioms that is Normally reserved.

Discuss how the shape/position of the Normal incurvation fluctuates when the meaconfident disconnection

increases/decreases or when the moderation increases/decreases.

Define the measureized rate or Z-score. Rate the Z-score, and use the Z-charges to do

comparisons.

Calculate probabilities and shave-off rates using the 68%-95%-99.7% (Empirical) Rule.

Identify the moderation, meaconfident disconnection, shave-off rate, affectlihood, and Z-charges on a Normal incurvation.

Use the Normal consideration to get percentiles (probabilities) for anxious examples and to get Z-scores

in manage to indicate shave-offs for ignorant examples using twain > and < in the inequalities.

Recognize whether a anecdote is a anxious or ignorant Normal division example, and perform

the mismisalienate calculations pomping emend notation, the primal affectlihood enumerateenance, and all

essential steps.

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Chapter 21: What is a assurance space-between?

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Define statistical corollary and illustrate when statistical corollary is used.

Explain what the assurance space-unmoulded moderations and whether the results allude to the population or

the case.

Calculate the loophole of fault and confirm the loophole of fault in a assurance declaration.

Explain what pattern of fault is balmy in the loophole of fault.

Determine whether a anecdote is improve described delay a symmetry or a moderation.

Use mismisalienate notation for symmetrys and moderations, twain in the population and the case.

Calculate a assurance space-unmoulded for a symmetry and for a moderation.

Describe how increasing/decreasing the case dimension or assurance flatten fluctuates the loophole of

fault (width of the assurance space-between).

Apply saving for using assurance space-betweens.

o Need a unmixed haphazard case.

o Axioms must be placid emendly.

o No outliers.

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Practice Exam Questions

These experience exam inquirys are not moderationt to be an wasting register. These are simply examples of

questions that possess been asked in the departed. You definitely should try achievementing through these examples

delay your trick equivocation, but construct confident that you use the Learning Objectives to form your trick equivocation

and to acceleration you discover other examples to experience. Your preceptor uses the Learning Objectives when

writing the exams. The odd-numbered examples in your quantity possess acceptances in the tail, and the

StatsPortal website has frequent majestic instrument to acceleration your considering, distinctly the Learning Curve

quizzes and the video succession. Remember that you are recognized to bear a 1-page (twain interests ok),

handwritten-in-your-own-handwriting, 8 ½” x 11” trick equivocation delay you to the exam. Your ole should

be on the trick equivocation, and it accomplish be rate 1 aim on the exam when you rotate it in.

The exemplification/sampling intention and ethics topics from Exam 1 are expressive throughout the perfect

semester and may pomp up on behind exams.

1. Before the 2008 presidential antagonism, the Gallup Poll asked a case of 1,000 fellow-creatures for

whom they would vote for president; 52% said Obama. The loophole of fault for a 95%

assurance space-unmoulded enunciated by intelligence reports of this poll was:

A) ±8%

B) ±6%

C) ±4%

D) ±3%

E) ±2%

Show your achievement:

2. “Margin of fault” in this position moderations that if tnear is no bias

A)

B)

C)

D)

E)

every case the Gallup Poll takes accomplish end at lowest this arrest to the verity.

environing half of the cases the Gallup Poll takes accomplish end at lowest this arrest to the verity.

environing 95% of all cases the Gallup Poll takes accomplish end at lowest this arrest to the verity.

the sampling rule is biased—otherwise the poll would regularly yield the emend acceptance.

tnear are important nonsampling faults—otherwise the poll would regularly yield the emend

answer.

3. A Gallup poll examineed 3,112 voters. An AP poll examineed 778 voters from the corresponding population

on the exact corresponding inquiry. How does the loophole of fault for a 95% assurance space-between

compare for the Gallup and AP polls?

a. The Gallup loophole of fault is bigger than the AP loophole of fault.

b. The Gallup loophole of fault is the corresponding as the AP loophole of fault.

c. The Gallup loophole of fault is smaller than the AP loophole of fault.

4. The moderation is 80 and the meaconfident disconnection is 10. What is the meaconfident charges for an observation

of 90? Pomp your achievement adown.

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Suppose that the BAC of scholars who swallow five beers varies from scholar to scholar according to a

Normal division delay moderation 0.07 and meaconfident disconnection 0.01. For inquirys 10 through 13, pomp

your achievement adown the inquiry and transcribe your acceptance in the sequence.

5. The intermediate 99.7% of scholars who swallow five beers possess BAC unmoulded what two aggregate?

6. What percent of scholars who swallow five beers possess BAC adown 0.09?

7. What BAC do the carrying 15% of scholars possess behind swallowing five beers?

8. Sketch a Normal incurvation for the example over delay moderation = 0.07 and meaconfident disconnection = 0.01.

Label your x-axis from 0.04 to 0.10 in 0.01 increments. Too pomp the how the top 15% of

students (from #7) would be represented on that Normal incurvation.

9. A poker illustrateer is dealt thin artisans for different hours. He decides to bet heavily on

the latest artisan of the slumbering on the basis that behind frequent bad artisans he is due for a

winner.

a)

b)

c)

d)

He’s equitable, owing the attractives possess to medium out.

He’s injustice, owing successive deals are refractory of each other.

He’s equitable, owing successive deals are refractory of each other.

He’s injustice, owing his expected attractives are $0 and he’s adown that now.

10. The affectlihood of an outend of a haphazard rarity is

a)

b)

c)

d)

either 0 or 1, continueing on whether the rarity can in-effect appear.

the symmetry of a very crave succession of repetitions on which the outend appears.

the moderation plus or minus two meaconfident disconnections.

the assurance flatten.

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In council axioms, a rowage consists of two or past men-folks who feed simultaneously and are allied by blood

or matrimony. Elect an American rowage at haphazard and enumerate the enumerate of fellow-creatures it contains. Near is

the assignment of probabilities for your fruit:

# of men-folks

Probability

2

0.42

3

0.23

4

0.21

5

0.09

6

0.03

7 or past

???

11. What is the affectlihood a rowage accomplish possess 7 or past fellow-creatures in it? Pomp your achievement adown.

12. What is the affectlihood a rowage accomplish possess past than 2 fellow-creatures in it? Pomp your achievement adown.

13. What is the affectlihood a rowage accomplish possess 3 or 4 fellow-creatures in it? Pomp your achievement adown.

14. What is the expected rate of the enumerate of rowage members? Pomp your achievement adown and

transcribe your acceptance in the unmitigated.

15. A dispose of cards contains 52 cards, of which 4 are aces. You are offered the succeedingcited determine:

haul one card at haphazard from the dispose. You win $10 if the card hauln is an ace. Otherwise

you occasion $1. If you construct this determine very frequent spells, what accomplish be the moderation fruit?

a)

b)

c)

d)

e)

environing -$1, owing you accomplish occasion most of the spell.

environing $9, owing you accomplish win $10 but occasion simply $1.

environing -$0.15, that is, on the medium you occasion environing 15 cents.

environing $0.77, that is, on the medium you win environing 77 cents.

environing $0 owing the haphazard haul yields you a equiconsultation bet.

16. A dispose of 52 cards contains 13 natures. Near is another determine: haul one card at

haphazard from the dispose. If the card hauln is a nature, you win $2. Otherwise, you occasion $1.

Compare this determine (ole it Determine 2) delay that of the prior inquiry (ole it Determine 1).

Which one should you elect?

a)

b)

c)

d)

e)

Wager 1, owing it has a eminent expected rate.

Wager 2, owing it has a eminent expected rate.

Wager 1, owing it has a eminent affectlihood of attractive.

Wager 2, owing it has a eminent affectlihood of attractive.

Both determines are akin indulgent.

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17. A psychologist reflects that registerening to Bach may acceleration fellow-creatures reflect. She yields subjects a set of

puzzles and measures how frequent they clear-up in 5 minutes period registerening to Bach. From axioms on

frequent fellow-creatures, the psychologist indicates a affectlihood copy for solving 1, 2, 3,4 , and 5

puzzles clear-upd. The expected rate she rates from this affectlihood copy is 2.6. The law of

liberal aggregate says

a) watch whether each of frequent subjects clear-ups a conundrum. The symmetry who clear-up a conundrum

accomplish be arrest to the expected rate.

b) if you watch five subjects in a row who clear-up simply one conundrum, the proximate different subjects are

mitigated to clear-up three or indelicate conundrums owing the medium must cling arrest to the expected

value.

c) the expected rate is emend simply in a haphazardized relatively exemplification.

d) watch frequent subjects and chronicles how frequent conundrums each clear-ups. The medium accomplish be arrest

to the expected rate.

The division of acmes of adult men is closely Normal delay moderation 69 inches and measure

disconnection 2.5 inches. Pomp your achievement. Answers delayout emend achievement accomplish not hold any merit.

18. What percent of all men are sooner than 64 inches?

19. How elevated is a man whose measureized acme is z = -0.3? Acceptance in inches.

20. What percent of all men are elevateder than a man whose acme is at the 60th percentile?

21. How elevated is a man who is in the 82nd percentile? Acceptance in inches.

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The casino diversion craps is installed on flattening two dice. Near is the assignment of probabilities to the sum of

the aggregate on the up faces when two dice are flattened:

Outcome

2

Probability 1/36

3

2/36

4

3/36

5

4/36

6

5/36

7

6/36

8

5/36

9

4/36

10

3/36

11

2/36

12

1/36

The most contemptible bet in craps is the “ignoring sequence.” A ignoring sequence bettor wins forthsucceeding a while if either a 7 or an

11 ends up on the primeval flatten. This is oleed a “natural.” Use this distinguishledge to acceptance inquirys 11

through 14.

22. What is the affectlihood of a probable?

a. 2/36

b. 6/36

c. 8/36

d. 12/36

e. 20/36

23. What is the affectlihood you do not flatten a 7?

a.

6/36

b. 28/36

c. 0

d. 30/36

e. 8/36

24. Gigi has flattened a probable on indelicate nearest tosses of the dice. This excites the gamblers standing

around the consideration. They should distinguish that:

a.

b.

c.

d.

e.

Gigi has a hot artisan, so she is past mitigated to flatten another probable.

The law of mediums says that Gigi is now cabandon mitigated to flatten another probable.

Rolls are refractory, so the luck of flattening another probable has not newfangled.

Four nearest probables are closely impracticable, so the dice are probably loaded.

They should not be surprised owing the affectlihood of indelicate nearest probables is 2/36.

25. The consideration over pomps a licit affectlihood copy owing:

a.

b.

c.

d.

e.

All the probabilities are unmoulded 0 and 1.

All the probabilities are unmoulded -1 and 1.

The sum of all the probabilities is correspondently 1.

Both A and C.

Both B and C.

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26. A diversion involving a two of dice pays you $4 delay affectlihood 16/36, costs you $2 delay affectlihood

14/36, and costs you $6 delay affectlihood 6/36. What is the expected rate of the equality of

specie you win or occasion behind one illustrate of the diversion? Pomp your achievement using 3 decimal places. An

acceptance delayout emend achievement accomplish hold no merit.

Fewer US teens steam, swallow than European peers: consider

Fewer teenagers in the United States steam and swallow compared to their European enumerateerparts, but

past use garbages, according to a University of Michigan consider released Friday.

Using axioms from 36 European enumerateries plus the United States, researchers institute that 27 percent of US

adolescents had consumed alcohol in the month anterior to nature quizzed by pollsters, compared to 57

percent of Europeans.

Twelve percent of American teens had steamd tobacco, compared to 20 percent for the Europeans,

according to the consider, the fifth of its bark since 1995 delay a aggregate of 100,000 scholars elderly 15 and 16

taking segregate.

"One of the reasons that smoking and swallowing rates unmoulded adolescents are so considerable inferior near than in

Europe is that twain behaviors possess been frugal and possess reached historically low flattens in the United

States," carry composer Lloyd Johnston said.

"But smooth in the prior years of the European examines, swallowing and smoking by American adolescents

was perfectly low by similarity," he said, adding as-well that "use of unfair garbages is perfectly a divergent

matter."

Eighteen percent of the Americans had used marijuana or hashish, a symmetry exceeded in Europe simply

in France (24 percent) and Monaco (21 percent).

On medium, simply ssmooth percent of girlish Europeans had used either pith.

Relatively indulgent admission to marijuana and slight awareness of its dangers illustrate the figures, according to

the responses that researchers placid from examine segregateicipants.

The Americans were too the biggest users of all other garbages as-well marijuana -- such as LSD, ecstasy

and amphetamines -- at 16 percent, compared to six percent opposite Europe.

"Clearly the United States has attained relatively low rates of use for cigarettes and alcohol, though not

as low as we would affect," Johnston said. "But the flatten of unfair garbage use by adolescents is tranquil exceptional

here."

15,400 teenagers in the United States took segregate in the examine, acrave delay at lowest 2,400 enumerateerparts in

each of the 36 European nations, the University of Michigan said in a declaration.

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27. What is the population of concern for this consider?

28. Ole the most mitigated pattern of fault that could application the discoverings in this consider. Illustrate your

choice.

29. What was the case dimension for individuals from the US for the floating year?

30. Rate a 90% assurance space-unmoulded (CI) for the symmetry of U.S. teenagers that had used

marijuana or hashish (intermittently for the floating year).

31. Suppose you were to fluctuate the assurance flatten in inquiry 4 to 95% using the corresponding case.

How would the assurance space-unmoulded fluctuate? No calculations essential.

a.

b.

c.

d.

The assurance space-unmoulded would be the corresponding width but shifted to the left.

The assurance space-unmoulded would be the corresponding width but shifted to the equitable.

The assurance space-unmoulded would possess the corresponding nature but would be ramble.

The assurance space-unmoulded would possess the corresponding nature but would be narrower.

32. What if the case dimension was simply 5000 fellow-creatures for the 90% assurance space-unmoulded in #4. How would

the assurance space-unmoulded fluctuate delay this smaller case dimension? No calculations essential.

a.

b.

c.

d.

The assurance space-unmoulded would be the corresponding width but shifted to the left.

The assurance space-unmoulded would be the corresponding width but shifted to the equitable.

The assurance space-unmoulded would possess the corresponding nature but would be ramble.

The assurance space-unmoulded would possess the corresponding nature but would be narrower.

33. A novel poll reported a assurance 95% assurance space-unmoulded of 52% ± 3%. The poll

was carried out by telephone, so fellow-creatures delayout phones are regularly embracing from the

sample. Any faults in the decisive results due to yet fellow-creatures delayout phones:

a.

b.

c.

d.

are moderate in the enunciated loophole of fault.

are in specification to the enunciated loophole of fault.

can be ignored, owing these fellow-creatures are not segregate of the population.

can be ignored owing this is a nonsampling fault.

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34. The specialty “95% assurance” moderations

a.

b.

c.

d.

our results are gentleman for 9% of the population of all adults.

95% of the population falls delayin the loophole of fault we enunciate.

the affectlihood is 0.95 that a haphazardly clarified adult falls in the loophole of fault we enunciate.

we got these results using a rule that yields emend acceptances in 95% of all cases.

35. Gallup polled 1,523 adults and 501 teens on whether they generally vulgar of allowable gambling.

63% of adults and 52% of teens said yes. The loophole of fault for a 95% assurance declaration

environing teens would be

a.

b.

c.

d.

e.

greater than for adults, owing the teen case is smaller.

cabandon than for adults, owing the teen case is smaller.

cabandon than for adults, owing tnear are fewer teens in the population.

the corresponding as for adults, owing they twain end from the corresponding case examine.

Can’t say, owing it continues on what percent of each population was in the case.

36. Which of the succeedingcited rules would wane the width of a assurance

space-unmoulded for a moderation, if all else clings the corresponding. You may elect past than one acceptance for

this inquiry.

a.

b.

c.

d.

Increase the flatten of assurance.

Increase the case dimension.

Decrease the flatten of assurance.

Decrease the case dimension.

37. A 95% assurance space-unmoulded indicates that:

a. 95% of the feasible case moderations (same-dimension cases) accomplish be moderate by the space-between.

b. 95% of the space-betweens artful using this arrangement installed on corresponding-sized cases from this

population accomplish embody the case moderation.

c. 95% of the feasible population moderations accomplish be moderate by the space-between.

d. 95% of the space-betweens artful using this arrangement installed on corresponding-sized cases from this

population accomplish embody the population moderation.

38. A nationally reserved school intelligencepaper conducts a examine unmoulded scholars nationwide every

year. This year, responses from a unmixed haphazard case of 204 school scholars to the inquiry

“About how frequent CDs do you own?” resulted in a case moderation of 72.8. Installed on axioms from

prior years, the editors of the intelligencepaper accomplish suppose a population meaconfident disconnection of 7.2.

What is a 95% assurance space-unmoulded for the population moderation enumerate of CDs owned by all school

students? Pomp your achievement.

a.

(65.6, 80.0)

b. (71.8, 73.8)

c. (72.0, 73.6)

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d. (72.3, 73.3)

39. The perfect aim of doing a assurance space-unmoulded is:

a. To get distinguishledge environing the case statistic.

b. To do a census.

c. To price the meaconfident disconnection.

d. To price the population parameter.

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Practice Exam Answers

1. D

2. C

3. C

4. 1

5. 0.04 and 0.10

6. 97.73%

7. 0.081

8. Pomp a Normal incurvation delay 0.07 in the intermediate and 0.04 to 0.10 noticeable in smooth increments at

proper spacing on either interest. A sequence should be hauln at 0.081, delay shading to the equiconsultation of that

sequence and the shading labeled delay “top 15%.”

9. B

10. B

11. 0.02

12. 0.58

13. 0.44

14. 3.14

15. C

16. A

17. D

18. 2.5% (or 2.27% using the consideration)

19. 68.25

20. 40

21. 71.25

22. C

23. D

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24. C

25. D

26. 0

27. All US and European teens

28. Response fault b/c fellow-creatures force lie (other acceptances are apparently, but accomplish continue on the

rationale)

29. 15,400

30. Case symmetry is 18% delay n = 15,400. The assurance space-unmoulded is (0.1749, 0.1851) using Z* =

1.645, but either 1.64 or 1.65 could be used.

31. C

32. C

33. B

34. D

35. A

36. B, C

37. D

38. B

39. D