Final answer:
To find the probability that more than 35 PC purchasers bought an HP computer, use the binomial distribution.
Step-by-step explanation:
The probability of success (buying an HP computer) is given as 23%, which can be written as
�
=
0.23
p=0.23, and the number of trials is
�
=
130
n=130.
The probability of more than 35 purchasers buying an HP computer is equivalent to finding
�
(
�
>
35
)
P(X>35), where
�
X is the number of purchasers buying an HP computer.
The formula for the probability mass function of a binomial distribution is:
�
(
�
=
�
)
=
(
�
�
)
⋅
�
�
⋅
(
1
−
�
)
�
−
�
P(X=k)=(
k
n
)⋅p
k
⋅(1−p)
n−k
where
(
�
�
)
(
k
n
) is the binomial coefficient, equal to
�
!
�
!
(
�
−
�
)
!
k!(n−k)!
n!
.
The probability of more than 35 purchasers buying an HP computer is given by:
�
(
�
>
35
)
=
1
−
�
(
�
≤
35
)
P(X>35)=1−P(X≤35)
Now, we can calculate this probability:
�
(
�
>
35
)
=
1
−
∑
�
=
0
35
(
130
�
)
⋅
0.2
3
�
⋅
(
1
−
0.23
)
130
−
�
P(X>35)=1−∑
k=0
35
(
k
130
)⋅0.23
k
⋅(1−0.23)
130−k
Calculating this sum involves a large number of terms, and it's typically more practical to use statistical software, calculators, or tables to find this cumulative probability.
If you have access to such tools, you can input the parameters of the binomial distribution (n, p) and calculate
�
(
�
>
35
)
P(X>35). If you don't have access to such tools, you may want to use statistical software or online calculators to perform the computation.