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

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    2022-01-07T02:26:44+00:00

    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%

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