15 February, 2013
Exan i IA
Math 1070
Tins exam will last 50 nunutes a.1i(l nisists of 13 probleiiis and 1 bonus
prol)leiil. Write yolli answers iii the 51(e prouided. All solutions nuist be
sufficiently justified to receive (rechit. You may use li sciciitifi( 01 grn.plimg
calcUlator 1111(1 O11C 3’’ X 5 not ecard. You iiiiy not. use any other iiotes or
texts. Good luck!
Name:
Section:
-
Advice: If you get stuck o a problem, don’t panic. Move on and come back to it later.
Page
Points
2
12
3
8
4
15
5
15
6
15
7
20
8
20
Total:
105
Score
1\’Iultiplc Choice: Circle
the aiisvcr
(1101(0 1
hat is either most accurate or best.
answers the
10t iON
(
1
1
1. (4 points) The picture 1)010W is a liistograni which describes the clixtributioll of a quaIl—
lit at ive variil 4c. Winch of the Iollowmg uiswcr choices best describes tins distribution?
A. Uniforni
B. Symmetric
C. Skewed to the left ®Skewed to the right
points) The figure below is a box plot. The arrow in the figure is pointing to the
feature of the box plot which corresponds to which numerical summary?
2. (4
A. Minimum
B. First Quartile @Median
D. Mean
E. Third Quartile
3. (4 points) The figure below is a scatterplot which shows the relationship between the
ages of husbands and their wives. Which of the values below is closest to the correlation
coefhicient (r) for this (lata?
A. r=—O.4
B. r=O.1 @r=O.8
D. r=O
Page 2
E. r=—O.8
1. (4 points) Suppose that a stl1(leult earns 10, 12, 8, and 13 points on her first four quizzes,
is 14
1Cs1)e(I iX1(lY. What must she get on her fift ii ([1hz so that liei nieaii (111W score
points?
A. 13
B. 20
C.:32
@27
E. 17
5. (4 points) A normal distribution is completely described by which two parameters?
A. Mean and Median
B. Standard Deviation and Variance
®Mean
and Standard Deviation
Page 3
Visiializiiig Distributioiis
6. (15 point ) II oxeiwrant z meaxiired I lie heights of 30 of his elassmates incl fouiid that
. The ineasiireiiieiits are listed below. Draw a
1
they were I)etwe ii 58 i1i(h 76 iiiclies I HI
hiist)grn ii with 6 n)tervaIs which represents this (lata.
58.0
65.0
69.2
6i.0 61.2 62.1
65.2 65.7 67.0
69.5 69.6470.1
62.7
67.3
72.3
63.2
67.5
72.5
63.2
67.8
72.5
64.3
68.0
73.1
64.9
68.5
74.7
J7
—--‘
&*
3
evcQ c
(9
4tu4
jO
Cf
L
S
4
3
I
(Th
1-o
7-
C)
I
Page 4
?(
65.0
69.2
76.0
7. (10 points) Guildeusteni (oulitcd dif-fcreiit colored beetles in his garden. His observa—
I 10115 are recorded ill the table below. Make a bar graph to show the relative amounts
of (lifl(1ellt colored beetles that lie saw.
[[_mberColor
of Beetles
Green
1
Red
5
B,eF*\es
Orange
4
L
Vi
A
4
Brown
8
Blac1J
13
cxrc
1,
2-
I
Qs
Coors
Numerical Summaries of Distributions
I
8. (5 points) Three students in a math course received the following scores (out of 100) on
the first midterm exam:
76,83,81
Given that the exam average for these three students is 80, calculate the standard devi
ation of the exam scores.
(i -o)
Page 5
1
11(’StioHx l)eloW:
1
9. (15 1)OilltX) Use the lohlowing (bun to answer the (
12, 7, 14, 10,9, 11
(a) Conipuite the iiiean of the ohseivatiouis.
—=
iZL
(b) Compute the median of the observations.
M
2-
(c) Compute the first and third quartiles of the observations.
Page 6
Normal
10.
Distributions
(10 points) The prices of honies iii the Kingdom of Deimiark follow a normal (listriblitioll
with a mean ol $1,000,000 and a staiidard deviation of $300,000. What percentage of
lioiiic (051 itiore Ihan $1 ,600,000?
¶_
,t
i
boo
QO
—
IOOO,D0D
3Q0,000
I— PC.oo)
.OZ2-
-
11. (10 points) The heights of 13-year-old girls are normally distribriteci with mean 62.6
inches and standard deviation 7.2 inches. Ophelia wants to be taller than 80o of the
girls her age so that she can be on the basketball team. How tall does she need to be?
.2)
Pc&
joS
9
zo (
9
.Qp.
Page 7
12. (15 poiiits) A re earclier wishes to use st,udeuts IQ’s to predict their SAT score. There
score
is a (olTelatiohl of 0.S2 between SAT score and IQ score. The average SAT Verbal
stauCard
is 500, with a standard (leViatioll of 100. The average IQ score is 100, with
(lcviatiol) 15. Calculate flue equation for the least squares regression Inie.
=
bv
=
i
5QO-(.)(IDD)
13. (5 points) A teacher wishes to predict his students’ performaice in a class based on
their scores on an aptitude test. He calculates that the least squares regression line is
grade in the course if they
= 26.768 + 0.644x. Use this equation to predict a student’s
received a score of 80 on the aptitude test.
l.:(Q—
o.fq
(go)
= o4-s.c2.
Page 8
I3oiiiis Qucstioii
14. (1 U points (bonus))
(
—
:i
—:r
ifi;>()
if r <0
Coiiipiitc the 1)O11iOi ol stall(lal(l iiornial obsei’vatioiis whose absohite value is bigger
t.lmii 1 7. i.e. Coniimte
P{N(0,1)I > 1.7}
p(- +P(x)
L t-i
Page 9