Question

The life of an electric component has an exponential distribution with a mean of 8.9 years. What is the probability that a randomly selected one such component has a life more than 8 years? Answer: (Round to 4 decimal places.)

Answer 1

`P(X>8)`

And for this case we can use the cumulative distribution function given by:

`F(x) = 1- e^(-\lambda x)`

And if we use this formula we got:

`P(X>8)= 1- P(X \leq 8) = 1-F(8) = 1- (1- e^{-(1)/(8.9) *8})=e^{-(1)/(8.9) *8}= 0.4070`

Explanation:

For this case we can define the random variable of interest as: "The life of an electric component " and we know the distribution for X given by:

`X \sim exp (\lambda =(1)/(8.9))`

And we want to find the following probability:

`P(X>8)`

And for this case we can use the cumulative distribution function given by:

`F(x) = 1- e^(-\lambda x)`

And if we use this formula we got:

`P(X>8)= 1- P(X \leq 8) = 1-F(8) = 1- (1- e^{-(1)/(8.9) *8})=e^{-(1)/(8.9) *8}= 0.4070`