Question

The lifespan of a car battery averages 5 years. Suppose the battery lifespan follows an exponential distribution. What is the probability that the battery lasts more than 3 years

Answer 1

The probability that battery lasts more than 3 years is $e^{-0.6 }$.

Parameter of Exponential Distribution

It is given that the average lifespan of the car battery = 5 years

⇒ μ = 5

And, we have to find the probability that the car battery lasts more than 3 years.

Now, the relation between the parameter of exponential distribution, λ and average, μ is given as,

1/ λ = μ

⇒ λ = 1/5

Calculating the Probability

The probability for the car battery to lasts more than 3 years is given by P(N>3). Here, N is the lifespan of the car battery.

P(N>3) = 1 - P(N≤3)

P(N>3) = 1-F(4)

Here, F is the exponential distribution  for the lifespan of the car battery.

P(N>3) = 1-(1-e^(-λn))

P(N>3) = $e^{-3/5}$

Thus, the required probability is,

P(N>3) = $e^{-0.6 }$

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