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

Review and Manner Exam Questions for Exam 2
Learning Objectives:
Chapter 17: Thinking encircling haphazard

Explain how stray flushts bekeep in the deficient run and in the desire run and how stray and
haphazard are not the selfselfcorresponding fiction.
Perform basic verisimilitude calculations using die flattens and invent tosses.
Define verisimilitude, and engage the rules for verisimilitude.
Explain whether the law of mediums is gentleman.
Explain how specific verisimilitude differs from a philosophical or tentative verisimilitude.

Chapter 18: Verisimilitude patterns

Define a verisimilitude pattern. Imagine a verisimilitude pattern for a sharp-end anecdote’s flushts.
Apply the basic rules of verisimilitude to a anecdote tenor.
Calculate probabilities using a verisimilitude pattern, including summing up probabilities or
subtracting probabilities from the aggregate.
Define a sampling arrangement.

Chapter 20: The seed edge: expected computes

Define expected compute, and consider the expected compute when abandoned a verisimilitude pattern.
Define the law of liberal mass, and interpret how it is irrelative from the fabulous “law of
averages.”
Explain how casinos and prophylactic companies remain in occupation and fashion capital.

Chapter 13: The Normal arrangement

Identify basis that is Normally reserved.
Discuss how the shape/position of the Normal deflexion varys when the plummet rupture
increases/decreases or when the medium increases/decreases.
Define the plummetized compute or Z-score. Consider the Z-score, and use the Z-accompute to do
comparisons.
Calculate probabilities and skin computes using the 68%-95%-99.7% (Empirical) Rule.
Identify the medium, plummet rupture, skin compute, verisimilitude, and Z-accompute on a Normal deflexion.
Use the Normal consultation to get percentiles (probabilities) for eager tenors and to get Z-scores
in classify to determine skins for unskilled tenors using twain > and < in the inequalities.
Recognize whether a anecdote is a eager or unskilled Normal arrangement tenor, and perform
the alienate calculations exhibitioning amend notation, the primal verisimilitude look, and all
needful steps.

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Chapter 21: What is a trust season?

Define statistical conclusion and interpret when statistical conclusion is used.
Explain what the trust season mediums and whether the results relate to the population or
the specimen.
Calculate the lip of fault and fulfill the lip of fault in a trust promulgatement.
Explain what cast of fault is expert in the lip of fault.
Determine whether a anecdote is meliorate picturesquely delay a adaptation or a medium.
Use alienate notation for adaptations and mediums, twain in the population and the specimen.
Calculate a trust season for a adaptation and for a medium.
Describe how increasing/decreasing the specimen extent or trust plane varys the lip of
fault (width of the trust season).
Apply saving for using trust seasons.
o Need a mere stray specimen.
o Basis must be unmoved amendly.
o No outliers.

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Practice Exam Questions
These manner exam inquirys are not mediumt to be an consumptive flatten. These are merely examples of
questions that keep been asked in the spent. You definitely should try started through these examples
delay your artifice shuffle, but fashion indispuconsultation that you use the Learning Objectives to imagine your artifice shuffle
and to succor you confront other tenors to manner. Your professor uses the Learning Objectives when
writing the exams. The odd-numbered tenors in your comignoring keep computeerparts in the end, and the
StatsPortal website has numerous majestic media to succor your con-overing, especially the Learning Curve
quizzes and the video course. Remember that you are allowed to convey a 1-page (twain partys ok),
handwritten-in-your-own-handwriting, 8 ½” x 11” artifice shuffle delay you to the exam. Your indicate should
be on the artifice shuffle, and it procure be price 1 sharp-end on the exam when you incsuccession it in.
The trial/sampling pur-pose and ethics topics from Exam 1 are essential throughout the total
semester and may exhibition up on succeeding exams.
1. Before the 2008 presidential hostilities, the Gallup Poll asked a specimen of 1,000 lowalty for
whom they would signification for president; 52% said Obama. The lip of fault for a 95%
trust season promulgated by counsel reports of this poll was:
A) ±8%

B) ±6%

C) ±4%

D) ±3%

E) ±2%

2. “Margin of fault” in this aspect mediums that if tless is no bias
A)
B)
C)
D)
E)

every specimen the Gallup Poll takes procure follow at conclusive this delay to the veracity.
encircling half of the specimens the Gallup Poll takes procure follow at conclusive this delay to the veracity.
encircling 95% of all specimens the Gallup Poll takes procure follow at conclusive this delay to the veracity.
the sampling system is biased—otherwise the poll would constantly grant the amend computeerpart.
tless are weighty nonsampling faults—otherwise the poll would constantly grant the amend

3. A Gallup poll reviewed 3,112 significationrs. An AP poll reviewed 778 significationrs from the selfselfcorresponding population
on the suiconsultation selfselfcorresponding inquiry. How does the lip of fault for a 95% trust season
compare for the Gallup and AP polls?
a. The Gallup lip of fault is bigger than the AP lip of fault.
b. The Gallup lip of fault is the selfselfcorresponding as the AP lip of fault.
c. The Gallup lip of fault is smaller than the AP lip of fault.
4. The medium is 80 and the plummet rupture is 10. What is the plummet accompute for an observation
of 90? Exhibition your performance under.
3

Suppose that the BAC of scholars who swallow five beers varies from scholar to scholar according to a
Normal arrangement delay medium 0.07 and plummet rupture 0.01. For inquirys 10 through 13, exhibition
your performance under the inquiry and transcribe your computeersegregate in the succession.
5. The medium 99.7% of scholars who swallow five beers keep BAC betwixt what two mass?

6. What percent of scholars who swallow five beers keep BAC under 0.09?

7. What BAC do the main 15% of scholars keep succeeding swallowing five beers?

8. Sketch a Normal deflexion for the tenor aloft delay medium = 0.07 and plummet rupture = 0.01.
Label your x-axis from 0.04 to 0.10 in 0.01 increments. To-boot exhibition the how the top 15% of
students (from #7) would be represented on that Normal deflexion.

9. A poker indicateer is dealt meagre operatives for different hours. He decides to bet heavily on
the conclusive operative of the waning on the grounds that succeeding numerous bad operatives he is due for a
winner.
a)
b)
c)
d)

He’s just, accordingly the engagings keep to medium out.
He’s wickedness, accordingly successive deals are fractions of each other.
He’s just, accordingly successive deals are fractions of each other.
He’s wickedness, accordingly his expected engagings are \$0 and he’s under that now.

10. The verisimilitude of an outfollow of a stray inquisitiveness is
a)
b)
c)
d)

either 0 or 1, being on whether the inquisitiveness can substantially appear.
the adaptation of a very desire course of repetitions on which the outfollow appears.
the medium plus or minus two plummet ruptures.
the trust plane.

4

In council basis, a race consists of two or further vulgar who subsist coincidently and are huskred by blood
or espousals. Cull an American race at stray and compute the enumerate of lowalty it contains. Less is
the assignment of probabilities for your effect:
# of vulgar
Probability

2
0.42

3
0.23

4
0.21

5
0.09

6
0.03

7 or further
???

11. What is the verisimilitude a race procure keep 7 or further lowalty in it? Exhibition your performance under.

12. What is the verisimilitude a race procure keep further than 2 lowalty in it? Exhibition your performance under.

13. What is the verisimilitude a race procure keep 3 or 4 lowalty in it? Exhibition your performance under.

14. What is the expected compute of the enumerate of race members? Exhibition your performance under and
transcribe your computeersegregate in the unmitigated.
15. A invest of cards contains 52 cards, of which 4 are aces. You are offered the forthcoming rest:
describe one card at stray from the invest. You win \$10 if the card describen is an ace. Otherwise
you cause \$1. If you fashion this rest very numerous seasons, what procure be the medium effect?
a)
b)
c)
d)
e)

encircling -\$1, accordingly you procure cause most of the season.
encircling \$9, accordingly you procure win \$10 but cause barely \$1.
encircling -\$0.15, that is, on the medium you cause encircling 15 cents.
encircling \$0.77, that is, on the medium you win encircling 77 cents.
encircling \$0 accordingly the stray describe grants you a reasonable bet.

16. A invest of 52 cards contains 13 characters. Less is another rest: describe one card at
stray from the invest. If the card describen is a character, you win \$2. Otherwise, you cause \$1.
Compare this rest (fawn it Rest 2) delay that of the anterior inquiry (fawn it Rest 1).
Which one should you promote?
a)
b)
c)
d)
e)

Wager 1, accordingly it has a excellent expected compute.
Wager 2, accordingly it has a excellent expected compute.
Wager 1, accordingly it has a excellent verisimilitude of engaging.
Wager 2, accordingly it has a excellent verisimilitude of engaging.
Both rests are equally fond.

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17. A psychologist gards that flattenening to Bach may succor lowalty gard. She grants subjects a set of
puzzles and measures how numerous they unfold in 5 minutes time flattenening to Bach. From basis on
numerous lowalty, the psychologist determines a verisimilitude pattern for solving 1, 2, 3,4 , and 5
puzzles unfoldd. The expected compute she considers from this verisimilitude pattern is 2.6. The law of
liberal mass says
a) heed whether each of numerous subjects unfolds a intricacy. The adaptation who unfold a intricacy
procure be delay to the expected compute.
b) if you heed five subjects in a row who unfold barely one intricacy, the present different subjects are
mitigated to unfold three or foul-mouthed intricacys accordingly the medium must remain delay to the expected
value.
c) the expected compute is amend barely in a strayized adjustmentately trial.
d) heed numerous subjects and chronicles how numerous intricacys each unfolds. The medium procure be delay
to the expected compute.
The arrangement of crisiss of adult men is approximately Normal delay medium 69 inches and plummet
rupture 2.5 inches. Exhibition your performance. Answers delayout amend performance procure not entertain any faith.
18. What percent of all men are deficienter than 64 inches?

19. How elevated is a man whose plummetized crisis is z = -0.3? Countersegregate in inches.

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

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

6

The casino amusement craps is established on flattening two dice. Less is the assignment of probabilities to the sum of
the mass 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 low bet in craps is the “ignoring succession.” A ignoring succession bettor wins unswervingway if either a 7 or an
11 follows up on the primitive flatten. This is fawned a “natural.” Use this counsel to computeersegregate inquirys 11
through 14.
22. What is the verisimilitude of a flushtual?
a. 2/36

b. 6/36

c. 8/36

d. 12/36

e. 20/36

23. What is the verisimilitude 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 flushtual on foul-mouthed unswerving tosses of the dice. This excites the gamblers standing
around the consultation. They should apprehend that:
a.
b.
c.
d.
e.

Gigi has a hot operative, so she is further mitigated to flatten another flushtual.
The law of mediums says that Gigi is now near mitigated to flatten another flushtual.
Rolls are fractions, so the haphazard of flattening another flushtual has not radical.
Four unswerving flushtuals are almost unusable, so the dice are probably loaded.
They should not be surprised accordingly the verisimilitude of foul-mouthed unswerving flushtuals is 2/36.

25. The consultation aloft exhibitions a real verisimilitude pattern accordingly:
a.
b.
c.
d.
e.

All the probabilities are betwixt 0 and 1.
All the probabilities are betwixt -1 and 1.
The sum of all the probabilities is suitablely 1.
Both A and C.
Both B and C.

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26. A amusement involving a span of dice pays you \$4 delay verisimilitude 16/36, costs you \$2 delay verisimilitude
14/36, and costs you \$6 delay verisimilitude 6/36. What is the expected compute of the equality of
capital you win or cause succeeding one indicate of the amusement? Exhibition your performance using 3 decimal places. An
countersegregate delayout amend performance procure entertain no faith.

Fewer US teens steam, swallow than European peers: con-over
Fewer teenagers in the United States steam and swallow compared to their European computeerparts, but
further use garbages, according to a University of Michigan con-over released Friday.
Using basis from 36 European computeries plus the United States, researchers fix that 27 percent of US
adolescents had consumed alcohol in the month prior to being 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 con-over, the fifth of its husk past 1995 delay a aggregate of 100,000 scholars old 15 and 16
taking segregate.
"One of the reasons that smoking and swallowing rates shapeless adolescents are so fur inferior less than in
Europe is that twain behaviors keep been degraded and keep reached historically low planes in the United
States," guide committer Lloyd Johnston said.
"But flush in the prior years of the European reviews, swallowing and smoking by American adolescents
was perfectly low by similitude," he said, adding however that "use of unfair garbages is perfectly a irrelative
matter."
Eighteen percent of the Americans had used marijuana or hashish, a adaptation exceeded in Europe barely
in France (24 percent) and Monaco (21 percent).
On medium, barely sflush percent of boyish Europeans had used either gist.
Relatively lenient advent to marijuana and unimportant awareness of its dangers interpret the figures, according to
the responses that researchers unmoved from review segregateicipants.
The Americans were to-boot the biggest users of all other garbages as-well marijuana -- such as LSD, ecstasy
and amphetamines -- at 16 percent, compared to six percent across Europe.
"Clearly the United States has attained correlationately low rates of use for cigarettes and alcohol, though not
as low as we would approve," Johnston said. "But the plane of unfair garbage use by adolescents is tranquil exceptional
here."
15,400 teenagers in the United States took segregate in the review, adesire delay at conclusive 2,400 computeerparts in
each of the 36 European nations, the University of Michigan said in a promulgatement.
8

27. What is the population of share for this con-over?

28. Indicate the most mitigated cast of fault that could impression the confrontings in this con-over. Interpret your
choice.

29. What was the specimen extent for living-souls from the US for the prevalent year?

30. Consider a 90% trust season (CI) for the adaptation of U.S. teenagers that had used
marijuana or hashish (frequently for the prevalent year).

31. Suppose you were to vary the trust plane in inquiry 4 to 95% using the selfselfcorresponding specimen.
How would the trust season vary? No calculations needful.
a.
b.
c.
d.

The trust season would be the selfselfcorresponding width but shifted to the left.
The trust season would be the selfselfcorresponding width but shifted to the just.
The trust season would keep the selfselfcorresponding character but would be straggle.
The trust season would keep the selfselfcorresponding character but would be narrower.

32. What if the specimen extent was barely 5000 lowalty for the 90% trust season in #4. How would
the trust season vary delay this smaller specimen extent? No calculations needful.
a.
b.
c.
d.

The trust season would be the selfselfcorresponding width but shifted to the left.
The trust season would be the selfselfcorresponding width but shifted to the just.
The trust season would keep the selfselfcorresponding character but would be straggle.
The trust season would keep the selfselfcorresponding character but would be narrower.

33. A new poll reported a trust 95% trust season of 52% ± 3%. The poll
was carried out by telephone, so lowalty delayout phones are constantly extreme from the
sample. Any faults in the last results due to except lowalty delayout phones:
a.
b.
c.
d.

are interjacent in the promulgated lip of fault.
are in adduction to the promulgated lip of fault.
can be ignored, accordingly these lowalty are not segregate of the population.
can be ignored accordingly this is a nonsampling fault.

9

34. The phrase “95% trust” mediums
a.
b.
c.
d.

our results are gentleman for 9% of the population of all adults.
95% of the population falls delayin the lip of fault we promulgate.
the verisimilitude is 0.95 that a strayly selected adult falls in the lip of fault we promulgate.
we got these results using a system that grants amend computeerparts in 95% of all specimens.

35. Gallup polled 1,523 adults and 501 teens on whether they generally approved of allowable gambling.
63% of adults and 52% of teens said yes. The lip of fault for a 95% trust promulgatement
encircling teens would be
a.
b.
c.
d.
e.

greater than for adults, accordingly the teen specimen is smaller.
near than for adults, accordingly the teen specimen is smaller.
near than for adults, accordingly tless are fewer teens in the population.
the selfselfcorresponding as for adults, accordingly they twain follow from the selfselfcorresponding specimen review.
Can’t say, accordingly it bes on what percent of each population was in the specimen.

36. Which of the forthcoming systems would wane the width of a trust
season for a medium, if all else remains the selfsame. You may cull further than one computeersegregate for
this inquiry.

a.
b.
c.
d.

Increase the plane of trust.
Increase the specimen extent.
Decrease the plane of trust.
Decrease the specimen extent.

37. A 95% trust season indicates that:
a. 95% of the practicable specimen mediums (same-extent specimens) procure be interjacent by the season.
b. 95% of the seasons simulated using this order established on selfsame-sized specimens from this
population procure embrace the specimen medium.
c. 95% of the practicable population mediums procure be interjacent by the season.
d. 95% of the seasons simulated using this order established on selfsame-sized specimens from this
population procure embrace the population medium.
38. A nationally reserved academy counselpaper conducts a review shapeless scholars nationwide every
year. This year, responses from a mere stray specimen of 204 academy scholars to the inquiry
“About how numerous CDs do you own?” resulted in a specimen medium of 72.8. Established on basis from
anterior years, the editors of the counselpaper procure postulate a population plummet rupture of 7.2.
What is a 95% trust season for the population medium enumerate of CDs owned by all academy
a.

(65.6, 80.0)

b. (71.8, 73.8)

c. (72.0, 73.6)
10

d. (72.3, 73.3)

39. The total sharp-end of doing a trust season is:
a. To get counsel encircling the specimen statistic.
b. To do a census.
c. To admire the plummet rupture.
d. To admire the population parameter.

11

1. D
2. C
3. C
4. 1
5. 0.04 and 0.10
6. 97.73%
7. 0.081
8. Exhibition a Normal deflexion delay 0.07 in the medium and 0.04 to 0.10 conspicuous in flush increments at
proper spacing on either party. A succession should be describen at 0.081, delay shading to the just of that
succession 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 consultation)
19. 68.25
20. 40
21. 71.25
22. C
23. D
12

24. C
25. D
26. 0
27. All US and European teens
28. Response fault b/c lowalty faculty lie (other computeerparts are ostensible, but procure be on the
rationale)
29. 15,400
30. Specimen adaptation is 18% delay n = 15,400. The trust season 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