Question

Assume that the average life of a particular brand of Diehard car battery is 5.7 years and that this time follows the exponential probability distribution. What is the probability that a randomly selected battery will have a life of less than 8.0 years?

Answer 1

75.43%

Explanation:

Para dar respuesta al ejemplo aplicamos la formula de distribución exponencial.

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

Where,

`\lambda` is the parameter of distribution and is equal to

`\lambda = (1)/(E)`, E is our Expected Value 5.7

`x= 8` (Our variable to search)

So we have,

`\lambda = (1)/(5.7) = 0.1754`

Then,

`P ( X < x ) = 1-e^((-\lamda* x))`

`P ( X < 8 ) = 1 - e^(-1.4032) = 0.7543`

Our probability to select a battery will have a life of less than 8 years is 75.43%