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Math 1307
Chapters 5,8,9, 10,21, an
Review for Final Exam
Statistics: The Science of Data
1. Twenty members of a health club who jog were asked how mapy miles they jog per week. The responses
are as follows.
# 12
15
27
4
40
7
22
12
19
25
13
21
23
33
18
6
8
34
17
16
. 4 b b , 7 , 8 , ~ a , l a , ~ q / s , / b , r 7 , 1 4 1 9 , ~ b3231,-q1a . 7 , 3 3 , 3 C f , Yo
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b. Construct a fiequency distribution
a. Construct a stemplot for this data.
Frequency
Class
0-9
4-
10- 19
g
40-29
5/
30-39
a
40-49
1
c. Construct a histogram of this information.
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s
F
r
d,is
to your calculator statistics package and find each of the following:
Now:
(Do not use @ouped d a t a 6 r this problem!)
d. mean =
18@b
d. standard deviation =
f. Q, =
I a,
g. Q t =
h. median = 1 ?t
j. maximum =
5
$0
24
i. minimum =
k. mode =
$
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4? ?L 2
2. A vending machine dispenses coffee into 8 ounce cups. The amount dispensed into these cups is
normally distributed with a.mean of 7.6 oz and a standard deviation of 0.4 oz.
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J %. Sketch a normal curve showing the mean and the points for +I- 3 sd's, +I- 2 sd's, and +I- 1 sd.
7.b - r
Lf= 7.A
2(a4)--6*f
1.6
-3 c 4)=b4
---=---
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+,$ = E D
?, '-tal.+j=fiq
7.~ f 3 (4)
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7.
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a
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b. Sketch a normal curve show.ing the niean and Q1and Qj
Use the information from the curves above to find each of the following:
c. What percent of cups contain between 7.2 ounces and 7.6 ounces of coffee?
a an& 8.0 = (-08%
b & d . . - - ? , a ~ ~ f i e ~ ? 4-
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7,
a-
d. What percent of the cups of coffee will overflow into the machine?
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,007"
8.9
02.
- CP 8 / 7 0 =
! L d
e. What percent of the cups will have less than 7.332 ounces of coffee?
f. If a cup is 'chosen at random, what is the robabilit that it will contain between 7.332 ounces
and 7.868 ounces?
,g,r
30%
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( 7 , 3 3 2 L X L Z S ~ ~ \-
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50
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16
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Probability: The Mathematics of Chance jd&
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3
3
. .3. Two fair dice are each numbered with a 3 on 1 side, a 2 on two sides, and a 1 on three sides. The
dice are rolled and the numbers on the two "up" faces are recorded.
b. Find the probability that both faces have 2's on them.
-
c. Now find the sum of the two "up" faces and show the sample space for this experiment.
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1%
oss .&I*
1
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d. Find the probability distribution of the random variable X (sum of the two faces).
e. Find the expected value of X.
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4. Three fair coins are tossed and the results are recorded.
construct a sample space for this experiment.
1
4 f-f 7
I-+ 77
T
0-8
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7 l+7
T 7
it
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-
v/m;
b. Use the information above to make a probability distribution for the random variable X = # heads.
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c. What is the theoretical probability of obtaining 2 heads?
9 corn
a
-:.
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d. What is the expected number of heads?
A
r
o(Y8)+
1
C3/d
a
e. This experiment was done 1 000 mes with the following results:
# heads
Frequency
+he
0
120
-&-om
a/yi
What is the approximate empirical probabil%tyof obtaining 2 heads?
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d
+a$/<
Voting and Social Choice
5. The children of Happy Faces Preschool are voting on their favorite classroom animal. The choices are
hamster (H), iguana (I), lemming (L), and salamander (S). The results of the election are given in the
following preference table:
"&a
Number of votes
3 First place
2 Second place
Third place
0 Fourth place
43
S
L
I
H
29
I
H
L
S
30
L
H
I
S
14
H
I
L
S
26
H
I
S
L
a. How many children voted in this eelcu-,
b. Does any animal have a majority of votes? If yes, which one?
I
yna.;\oc: C
;7
% -guires
71
l V 2 =
3
%
has
00 c ! & L u d t ,
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($10./+=a64/'-l =
animal wins if the plurality method is used? 1
@
L = 3 0
-5 hs+ h r
->
m
_CC=
~
d
~
L-@L
' i
~
~ ( S o - ~ & r n w * b >
d. Which animal wins if the Borda count method is used?
6. A group of people were asked to taste test and rank three different brands of apple jelly. The preference
table is shown below: . .Number of votes
First place
second place
Third place
6
A
A - C
B
B
7
C
CI
+
a. How many people took part in this taste test?
8.t 7+ 6 =
b. ~ i t e r m i n the
e winner if the Condorcet method is used.
*
s- =
c. If the Hare method is used, the winner is C (you do not have to show this - I gave it to you).
Could the people who least prefer C (that is, ranked C last) vote insincerely in some way to
change the outcome so that one of their more preferred choices wins? You must show work!
C
P
I
7. Suppose there are four classes of voters that rank four candidates as follows:
a. Which candidate is the plurality winner?
fi=s
& = L a
-z I?"4
b. %~ch candid te is the plurality runoff winner? --+ad<&
Your Money and Resources
8. Find each of the following:
a. Using the Rule of 72, find the approximate number of years it takes an investment to double if the
account pays 6.25% interest per year.
b. A credit card bill shows a balance of $2500 with a monthly interest rate of 1.53%. Calculate each of
- the following:
=
3
m=rL
no+
rds.
&&a
i. A P R z
z
AXJ~L
ii. EAR
= ( I $ Ljm-I
c~+,,y
la
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QPR-IP~~L?~
8
0
El+( = 19.4l?%
9. Jane deposits $2,000 annually into a Roth IRA that earns 6.85% compounded annually. (The interest
earned on a Roth IRA is tax free.) Due to a change in employment, these deposits stop after 10 years.
'
Jane does not take the money out of this account when she changes jobs. Even though she does not add
any more money to the account, the investment continues to earn interest until she retires 25 year after
the last deposit was made.
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t 1 ( l o \ = / -:-_c = ~ O L % ~ = , O ~ & =
5
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b. Calculate the amount of money in the account at the time Jane retires.
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e
( ~ t ~ b ~ ~ f i
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10
2 d
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10. A family purchased a home for $80,000. The home was financed by paying 20% down and signing a
30-year mortgage at 9% annual interest, compounded monthly on the unpaid balance. The current net
market value of the house is $120,000.
80 O O O C ~ ~ O
= \/ b ~ o D
.&
A= g o o o o - / L , 000 = b $ 0 0 0
lad. Calculate the mqnthly payments for the loan.
b. Calculate the interest that will be paid on this loan over the 30 year mortgage period.