The lifetime of a bearing (in years) follows the Weibull distribution with parameters α = 1.5 and β = 0.8.

a. What is the probability that a bearing lasts more than 1 year?

b. What is the probability that a bearing lasts less than 2 years?

Step 1 of 3:

It is given that lifetime of a bearing( in years) follows weibull distribution with =1.5 and

=0.8.

Let us denote the lifetime of the bearing as X. Then X~Weibull(=1.5,=0.8).

The probability mass function of X is given by,

P(Xx)=1-for x>0

=0 for x0

Step 2 of 3:

(a)

Here we have to find the probability that the lifetime of the bearing is more than 1 year.

That is,we have to find P(X>1)

P(X>1)=1-P(X1)

=1-[1-]

=

=

=0.4900

Thus,probability that the lifetime of bearing is more than 1 year is 0.4900.