Question

Suppose a car radiator useful lifetime has Weibull distribution with β = 1.5 and the mean lifetime of 150,000 miles. John has just bought a used car with 180,000 miles and original radiator which is still good. What is the probability that it’s going to last at least 20,000 miles more before needing replacement?

Answer 1

a weibul distribution has 3 parameters

1. which is called the share parameter it is also called the slope parameter as which is the slop in the probability plot

if which means that the distribution has a failure that increases over the time. here

2. Scale parameter 1,50,000 miles here.

3 Location parameter here

The distribution function of X is

we need to find out the life of the car radiator which go above 20000 miles than 180000 miles that means x goes at least 200000 miles so the function becomes

we need to find the P(X200000 miles ) = 1-P(X

whih is =

==

=0.215