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AP Statistics
Test Ch 6,7 REVIEW
Name
Part I - Multiple Choice (Questions 1-10) - Circle the answer of your choice.
1.
Family size
can be represented
by the random variable
X.
Determine the average family size.
X
2
J
4
5
Pfi)
17
.41
.26
.10
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x'eG)
@) 2.ea
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(e)
3.86
2. Suppose the average height of policemen is 71 inches with a standard deviation of 4 inches, while the average for policewoman is
66 inches with a standard deviation of 3 inches. If a committee looks at all ways of pairing up one male with one female officer, what
will be the mean and standard deviation for the difference.in he.igtr]!! {or the set of possible partners?
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Mean of 5 inches with a standard deviation of I inch. \v
erjolfo.c,trn0\+,
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Mean of 5 inches with a standard deviation of 3.5 inches
fZ6ilV""n of 5 inches with a standard deviation of 5 inches.
-- &,ror. - &uto*,"= 7l - tao =
/r^-r*oo
V U"un of 68.5 inches with a standard deviation of 1 inch.
(e) Mean of 68.5 inches with a standard deviation of 3.5 inches
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(a)
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-
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5
:
2b
I
3. My wife's friend, Karen, and her husband really want to have a baby girl. Because of financial consideratiols, they decide they
will have children either until the.v have a girl or a total o-f 3 children if the probability of having a boy or girl is equally likely,
determine the expected number of boys. [...piease note, as soon as they have a girl, they stop having kidsl Draw a tree diagram!]
(a) 0.5
(b) 0.75
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(e)
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4. Which of the following are true statements?
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By the law of large numbers, the mean of a random variable will get closer and closer to a specific value
The standard deviation ofa random variable is never negative.
The standard deviation ofa random variable is 0 only ifthe random variable takes a lone single value.
II
III
(c) II and III
(d) II and III
(a) I and
(b) I and
@t,II,
5.
IfP(X)
andlII
: 0.23 and P(X and Y) : 0.12 -d 3G,orY)a4,
[I would draw a.Venn Diagram if FweT6ffi
(a) 0.23
(b) 0.52
ffi;;
c
find P(Y ).
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or.olcth,.t ir .
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e
I
Use the following information for questions 6-8. The independent random variables X and Y are defined by the following probability
distribution tables.
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'l
x
P(X)
.6
'P^ffi;
6
Y
I
P(v)
.3
the mean
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(d) e
(e)
3
.
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v(
LQ
3.
5
1
.2
.J
.4
i! owc 5
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7. Which of the following is
(a)
(b)
o+\
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o
ft,i\s.qc --
I
J
^'l .- 2.i+E.l
4.3
5.1
2
r 3.21
,4.
=
&x * &y
\,
(a
8e6* {,
orx+Y
7. Determine the standard deviation of 3Y + 5
(a) .44
(b) 3.62
(c)
6-:
p!
true concerning discrete probability distribution?
The probability of any specific value is between 0 and 1, inclusive.
The mean of the distribution is between the smallest and largest value in the distribution.
The sum of allprobabilities is l.
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g. The amount of pollutants a factory dumps into a river is approximately normally distributed with a mean of 2.43 and a standard
deviation of 0.88 tons. What is the probability that it dumps more than 3 tons?
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(c) 0.6500 doottttr'
ial o.ztsz
(e) 0.7422
9.
lf
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''T"'
P
o
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gg
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candok'tal*,b\r,s
gA '
arandomly selected person from this table is wealthy, what is the probability he or she is a Republican?
Ranrrhlicar:
Wealthy
-ffit-Wealtf,
Riti?
(c)
0.1s99
(d) 0.8401
(e) I thought all Republicans
were wealthy.
reyvr
87
72
J5
418
501
90
5o\
617
%
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Part
II -
Free Response (Questions
ll-12) - Show your work and explain your results clearly.
t0. Suppose the probabiiity that someone will make a major mistake on an income tax return is 0.2. An Internal Revenue
Service (IRS) agent plans to audit twenty returns and determine how many had a major mistake.
a.
Define an appropriate assignment of random digits and using the given random number table, simulate (and clearly
label) this situation 4 times.
:8.
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dtttt L-1 = 1o m.r{alcr-ffoZ. .r*,-;
a
08424 44753 77377 28744 75592 08563 79140 924s4
2o hos i nil6Ffcr.
53645 66812 6t421 47836
3rd bto.kot 2o hrl
20 yoa 3 m.s{otrs
2al
2609 15373 98481 14s92
tl.lr+ri.,t,(?-o
3
rnclakes
b.
Based on your results, what is the expected number of returns with a major mistake?
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t
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1. Airlines routinely overbook flights
because they expect a certain number of no-shows. An airline runs a 5 p.m. commuter
flight from Washington, D.C. to New York City on a plane that holds 38 passengers. Past experience has shown that if 4l
tickets are sold for the flight, then the probability distribution for the number who actually show up for the flight is as shown
in the table below.
Sqn*,t ,{q.."6 3gtosll
Number who
2**t flP*,rr /^y9,# tS
/rnoqroiD!'
YV
Probabiiitv
O^g-tos
Assume that 4l tickets are sold for each flight.
a.
There are 38 passenger seats on the flight.
wh"t
will get a seat?
i,ffilllh$Xf"ssensers
who show up ror this night
What is the expected number of no-shows for this flight?
e(gu*)i*o '?
'rro '05 'ot'o\
ts are filled on
= q.t
a
what is the
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only 36 passengers showed up
12. Ap Statistics test scores on Random Variables
Score :
are described by the following probability distribution.
*
P(Score)
(a)
40
50
60
t0
80
0.1
0.2
0.3
0.3
0.1
Determine the
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rx
--
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not be denied admission to the
(b) Mr. Custer, in yet another act of benevolence, decides to scale the scores so his students will
*
20
1'5 Score '
college of theii choice. He decides the actual grades will become: Grade:
(i)
Determine the mean and variance of the
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(c)
Suppo.se three Scores were
(i)
"/
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(ii) Which Score(s), if any, did not increase?
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Grades
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randomly (and
)
lry!ggg$!!)
selected'
Determine the mean and variance of the total of the three Scores.
4"w'- h**\.X3
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o{gr' fi**rr*r= l4+t4+tz1' 6t/
(ii) What is the probability that the average of the three
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scores is greater than
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