Respuesta :
Answer:
The probability that a car battery lasts more than 36 months is 0.4066.
Step-by-step explanation:
Let X = the useful life of a particular car battery.
The decay parameter is, λ = 0.025.
The random variable X follows an Exponential distribution with parameter λ = 0.025.
The probability density function of X is:
[tex]f(x)=0.025e^{-0.025x};\ x>0[/tex]
Compute the probability that a car battery lasts more than 36 months as follows:
[tex]P(X>36)=\int\limits^{\infty}_{36} {0.025e^{-0.025x}} \, dx[/tex]
[tex]=0.025\int\limits^{\infty}_{36} {e^{-0.025x}} \, dx[/tex]
[tex]=0.025 |\frac{e^{-0.025x}}{-0.025}|^{\infty}_{36}\\[/tex]
[tex]=|-e^{-0.025x}|^{\infty}_{36}\\[/tex]
[tex]=|-0+e^{-0.02536}|^{\infty}_{36}\\[/tex]
[tex]=|-0+e^{-0.02536}|^{\infty}_{36}\\=0.4066[/tex]
Thus, the probability that a car battery lasts more than 36 months is 0.4066.
