The lifetime of a cooling fan, in hours, that is used in a computer system has the Weibull distribution with α = 1.5 and β = 0.0001.

a. What is the probability that a fan lasts more than 10,000 hours?

b. What is the probability that a fan lasts less than 5000 hours?

c. What is the probability that a fan lasts between 3000 and 9000 hours?

Step 1 of 3:

The lifetime of a cooling fan that is used in a computer has weibull distribution with .

We have to find

The Probability that fan last more than 10,000 hours.The Probability that fan last less than 5000 hours. The Probability that fan last between 3000 and 9000 hours.Step 2 of 3:

Let T be the lifetime of the fan which follows weibull distribution with parameters and .

So the pdf of T is

f(t) = , .

= (1.5) (0.0001

And the density function of T is

F(t) = P(

= 1-

= 1-

F(t) = 1-

Probability that fan last more than 10,000 hours.

P(T>10,000) = 1- P(

= 1- F(10,000)

= 1- (1- )

=

= 0.3679

P(T>10,000) = 0.3679

Therefore the probability that fan last more than 10,000 hours is 0.3679.