NE115  Final Exam Final Practice
1. Disks of polycarbonate plastic from a supplier are analyzed for scratch resistance and
shock resistance. The results of a sample of 150 disks are summarized below:
Shock Resistance
High
Low
High
60
30
Scratch Resistance
Low
40
20
What is the probability that a randomly selected disk demonstrates high resistance
to scratches and/or high resistance to shocks?
a) 0.67
b) 0.57
c) 0.87
d) 0.77
e) 0.97
Answer:
Sample size n = 150
A: high resistance to scaratches
B: high resistance to shocks
Probability that a random selected disk demonstrates high resistance to scaratches and/or
high resistance to shocks = P(A U B) = P(A) + P(B)  P(A ∩ B) = 100/150
+ 90/150 
60/150 = 0.87
2. An analysis of 17 pairs of data produced a least squares regression line with equation
x
y
2
17
+
=
∧
. What is the fitted value when
x
= 3?
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3. A set of data pairs has the following summary statistics:
,
52
,
30
=
=
y
x
S
xx
= 3, S
yy
= 2
,
and
r
= 1/2. What is the equation for the least squares regression line in terms of
x
and
y
?
(to the nearest tenth)
a)
x
y
3
1
=
∧
b)
x
y
2
1
=
∧
c)
x
y
4
3
5
.
27
+
=
∧
d)
x
y
4
3
5
.
7
+
=
∧
e)
x
y
5
2
40
+
=
∧
Answer:
2247
.
1
)
2
)(
3
(
)
5
.
0
(
2
2
2
2
=
⇒
=
⇒
=
xy
xy
yy
xx
xy
S
S
S
S
S
r
40
)
30
(
408
.
0
52
408
.
0
3
2247
.
1
1
0
1
≈

=

=
=
=
x
y
β
β
β
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 Spring '10
 Elkamel
 Normal Distribution, Variance, Sxx, Syy, d'Arcy

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