3. The time until failure of a certain type of electrical component is assumed to follow an exponential

distribution with a mean of 4 years. The manufacturer replaces all components that fail under

warranty.

A. (3 Points) What percentage of the components will fail within one year?

B. (3 Points) What is the probability that a randomly selected component will last more

than 2 years?/nC. (5 Points) Twenty-five percent of the components have a lifetime longer than c. Calcu-

late c./nD. (5 Points) The manufacturer can increase the lifetime of the component by redesigning

it. Assuming the lifetime of the component follows an exponential distribution, what does

the mean time until failure have to be in order for the probability that the component

lasts at least two years is 95 percent.