f the number of kilometers that a car can run before its bat

f the number of kilometers that a car can run before its battery wears out is exponentially distributed with an average value of 10,000 km and if the owner desires to take a 5000 km trip, what is the probability that he will be able to complete his trip without having to replace the car battery? Assume that the car has been used for same time.

Solution

X - no of kms that a car can run before its battery wears out

is exponential with mean = 10,000 km.

the probability that he will be able to complete his trip without having to replace the car battery

= P(X<5000)

= 1-e^-5000/10000 (cumulative prob for exponential)

= 1- 0.6065

= 0.3935