Answer:
75.43%
Step-by-step explanation:
Para dar respuesta al ejemplo aplicamos la formula de distribución 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%
