Jones figures that the total number of thousands of miles that an auto can be driven before it would need to be junked is an exponential random variable with parameter. fn. Smith has a used car that he claims has been driven only 10,000 miles. If Jones purchases the car, what is the probability that she would get at least 20,000 additional?

0.3678

Step-by-step explanation:

Jones figures that the total number of thousands of miles that an auto can be driven before it would need to be junked is an exponential random variable with parameter 1/20. Smith has a used car that he claims has been driven only 10,000 miles. If Jones purchases the car, what is the probability that she would get at least 20,000 additional miles out of it?

Given that the total number of thousands of miles (X) that an auto can be driven

before it would need to be junked is an exponential random variable with parameter 1/20.

=> X ≅ Exponential (λ = 1/20)

=> f (x) = 1/20 * e^ (-x/20), 0 < x < ∞

=> F (X) = P{X < x} = 1 - e^ (-x/20)

The probability that she would get at least 20,000 additional miles out of it.

P{X > 20} = 1-P{X < 20}

P{X > 20} = 1 - (1 - e^ (-20/20))

= e^ (-1)

= 0.3678