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ISyE 2027
Probability with Applications
Fall 2006
R. D. Foley
Homework 10
November 30, 2006
not due on Tuesday
1. Suppose all trucks heading south on I24 near Monteagle, Tennesse are inspected before descending
the mountain. What would be a reasonable guess as to the distribution of each of the following: (a)
the number of trucks inspected until a truck is found with a safety violation? (b) the number of trucks
arriving to the inspection facility between midnight and 1 a.m. tonight? (c) the number of trucks that
pass the safety inspection out of the ﬁrst 30 trucks arriving after midnight tonight? (d) the combined
weight of the next 15 trucks? (e) the length of time until a Mack truck arrives that is driven by a
person named Mack.
2. Suppose
Z
has a standard normal distribution. Compute (a) Pr
{
Z
≤
1
.
44
}
, (b) Pr
{
Z
 ≤
1
.
44
}
, (c)
Pr
{
Z >
1
.
44
}
, (d) Pr
{
Z
= 1
.
44
}
, and (e) ﬁnd the value of
x
such that Pr
{
Z

> x
}
=
.
05.
3. Suppose
X
is normally distributed with mean 2 and variance 100. Compute (a) Pr
{
X
≤
9
}
, (b)
Pr
{
X

>
9
}
, and ﬁnd the value of
x
such that Pr
{
X

2

/
3
> x
}
=
.
05.
4. Suppose
Y
is normally distributed with mean
μ
and variance
σ
2
>
0. Compute Pr
{
μ

kσ < Y < μ
+
kσ
}
for
k
= 0
,
1
,
2
,
and 3.
5. Let
Z
1
,...,Z
n
be i.i.d. standard normal random variables. It can be shown that if
m
is an even
number, then
E[
Z
m
] =
m
!
[2
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