NAME: KEY
Stat 205 Exam I
There are four problems total. Each lettered part of a problem is worth 6 points; there are 120
points total. However, your exam grade is out of 100 points, so there are 20 points of possible
extra credit for this exam. Write clearly and show steps for partial credit. This exam is open book.
1. The time to completion of the Rome marathon in 1996 is approximately normal with mean
μ
= 230
minutes and standard deviation
σ
= 36
minutes. Let
Y
be the time from a randomly
selected runner at this race.
(a) What is the probability of a randomly selected runner completing the race in under
three hours, Pr
{
Y <
180
}
?
Answer
:
Pr
{
Y <
180
}
=
Pr
Y

230
36
<
180

230
36
=
Pr
{
Z <

1
.
39
}
=
0
.
0823
.
(b) What is the probability of a randomly selected runner completing the race within three
to four hours, Pr
{
180
< Y <
240
}
?
Answer
:
Pr
{
180
< Y <
240
}
=
Pr
180

230
36
<
Y

230
36
<
240

230
36
=
Pr
{
1
.
39
< Z <
0
.
28
}
=
Pr
{
Z <
0
.
28
} 
Pr
{
Z <

1
.
39
}
=
0
.
6103

0
.
0823
=
0
.
528
(c) What is the probability of a randomly selected runner completing the race with a time
over five hours?
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '09
 Hendrix
 Normal Distribution, Standard Deviation

Click to edit the document details