Question

The time to failure (in hours) of fans in a personal computer can be modeled by an exponential distribution with l=0.0003

a. What proportion of the fans will last at least 10,000 hours?
b. What proportion of the fans will last at most 7000 hours?

Answer 1

Answer: 0.0497870 ; 0.87754

Explanation:

Given that :

λ = 0.0003

Defining a continuous distribution function :

F(x) = 1 - e^-λx = 1 - e^-0.0003x ; x ≥ 0

a. What proportion of the fans will last at least 10,000 hours?

P(x ≥ 10000) = e^-0.0003(10000) = 0.0497870

b. What proportion of the fans will last at most 7000 hours?

P(x ≥ 7000) = 1 - p(x ≤ 7000) = 1 - e^-0.0003(7000)

1 - 0.12245642825 = 0.87754