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Examples for 09/20/2007
Fall 2007
1.
A large class took two exams. Suppose the exam scores X (Exam 1) and
Y (Exam 2) follow a bivariate normal distribution with
μ
1
= 70,
σ
1
= 10,
μ
2
= 60,
σ
2
= 15,
ρ
= 0.6.
a)
A students is selected at random. What is the probability that his/her score
on Exam 2 is over 75?
P
(
Y > 75
) = P
(
Z >
15
60
75

) = P
(
Z > 1.00
) =
0.1587
.
b)
Suppose you're told that a student got a 80 on Exam 1. What is the
probability that his/her score on Exam 2 is over 75?
Given X = 80, Y has Normal distribution
with mean
( )
70
80
10
15
6
.
0
60

+
⋅
⋅
=
69
and variance
( )
2
2
15
6
.
0
1
⋅

=
144 ( standard deviation 12 ).
P
(
Y > 75
 X = 80
) = P
(
Z >
12
69
75

) = P
(
Z > 0.50
) =
0.3085
.
c)
Suppose you're told that a student got a 66 on Exam 1. What is the
probability that his/her score on Exam 2 is over 75?
Given X = 66, Y has Normal distribution
with mean
( )
70
66
10
15
6
.
0
60

+
⋅
⋅
=
56.4
and variance
( )
2
2
15
6
.
0
1
⋅

=
144 ( standard deviation 12 ).
P
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This note was uploaded on 04/29/2010 for the course STAT stat 420 taught by Professor Stepanov during the Spring '07 term at University of Illinois at Urbana–Champaign.
 Spring '07
 STEPANOV
 Normal Distribution

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