Solutions to Homework 5:
1.
In the World Cup soccer match, the average is 2.7 goals per game. In a particular game,
let X be the number of goals.
a. If you want to find the probability of x goals, should you use Binomial or
Poisson, Why?
Since the lamda is less than 7, the Poisson is an appropriate approximation of the
binomial.
b. What is the probability of at least one goal?
P(x≥1) = 1 – P(x = 0) = 1 
9328
.
0
067
.
0
1
!
0
7
.
2
0
7
.
2
=

=

e
c. What is the probability of more than three goals?
P(x > 3) = 1 – P(x ≤ 3) = 1 –(
)
!
3
7
.
2
!
2
7
.
2
!
1
7
.
2
!
0
7
.
2
3
7
.
2
2
7
.
2
1
7
.
2
0
7
.
2




+
+
+
e
e
e
e
=


067
.
0
1
0.18144 – 0.2449 – 0.2204 = 0.28601
d. Construct the probability distribution (graph) and describe its shape.
The distribution is somewhat bell shaped, but positively skewed.
2. It is estimated that 0.5 Percent of the callers to the Customer Service department of Dell,
Inc., will receive a busy signal. What is the probability that of today’s 1,200 callers at least
5 received a busy signal?
π = 0.005;
n = 1200
λ = 0.005*1200 = 6
P( x ≥ 5) = 1 – P( x < 5) = 1 – (
)
!
4
6
!
3
6
!
2
6
!
1
6
!
0
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 Spring '08
 Martin
 Probability, Variance, Probability theory, Corr

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