Answer:
a) 
In order to find this probability we can use excel with the following code:
=GAMMA.DIST(40;5,8,TRUE)-GAMMA.DIST(1,5,8,TRUE)
And we got:
b) 
In order to find this probability we can use excel with the following code:
=1-GAMMA.DIST(40,5,8,TRUE)
And we got:
Step-by-step explanation:
Previous concepts
The Gamma distribution "is a continuous, positive-only, unimodal distribution that encodes the time required for 
events to occur in a Poisson process with mean arrival time of 
"
Solution to the problem
Let X the random variable that represent the lifetime for transistors
For this case we have the mean and the variance given. And we have defined the mean and variance like this:
(1)
(2)
From this we can solve and [/tex]\beta[/tex]
From the condition (1) we can solve for and we got:
(3)
And if we replace condition (3) into (2) we got:
And solving for 
And now we can use condition (3) to find
So then we have the parameters for the Gamma distribution. On this case 
Part a
For this case we want this probability:
In order to find this probability we can use excel with the following code:
=GAMMA.DIST(40;5,8,TRUE)-GAMMA.DIST(1,5,8,TRUE)
And we got:
Part b
For this case we want this probability:
In order to find this probability we can use excel with the following code:
=1-GAMMA.DIST(40,5,8,TRUE)
And we got:
. Note that infinity
(or
itself isn't a real number. The round brackets indicate that both endpoints are excluded from the from the interval.
is
(both ends are excluded.) The set of all real numbers greater than (not equal to)
.
connects two intervals.
