Question

The life (in months) of a certain computer component has a probability density function defined by f(x)=\frac{1}{4} e^{-x / 4} for x in [0, infty). Find the probability that a component randomly selected will last between 10 and 20 months?

Answer 1

The probability that a component randomly selected will last between 10 and 20 months is approximately 0.0737.

Step-by-step explanation:

To find the probability that a component randomly selected will last between 10 and 20 months, we need to integrate the probability density function f(x) = (1/4)e^(-x/4) over the interval [10, 20].

The probability is given by:

P(10 < x < 20) = ∫(10 to 20) (1/4)e^(-x/4) dx

Using integration techniques, the integral evaluates to 0.0737. Therefore, the probability that a component randomly selected will last between 10 and 20 months is approximately 0.0737.