## 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?

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4 months 2022-01-07T02:25:33+00:00 1 Answer 0

75.43%

Step-by-step 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

$$\lambda = \frac{1}{E}$$, E is our Expected Value 5.7

$$x= 8$$ (Our variable to search)

So we have,

$$\lambda = \frac{1}{5.7} = 0.1754$$

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%