## Assume that the average life of a particular brand of Diehard car battery is 5.7 years and that this time follows the exponential probabilit

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?

in progress
0

Math
4 months
2022-01-07T02:25:33+00:00
2022-01-07T02:25:33+00:00 1 Answer
0
## Answers ( )

Answer:75.43%

Step-by-step explanation:Para dar respuesta al ejemplo aplicamos la formula de distribuciĆ³n exponencial.

[tex]P= 1- e^{-\lambda x}[/tex]

Where,

[tex]\lambda[/tex] is the parameter of distribution and is equal to

[tex]\lambda = \frac{1}{E}[/tex], E is our Expected Value 5.7

[tex]x= 8[/tex] (Our variable to search)

So we have,

[tex]\lambda = \frac{1}{5.7} = 0.1754[/tex]

Then,

[tex]P ( X < x ) = 1-e^{(-\lamda* x)}[/tex]

[tex]P ( X < 8 ) = 1 – e^(-1.4032) = 0.7543[/tex]

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