The length of time between breakdowns of an essential piece of equipment is an important factor in deciding on the amount of auxiliary equipment needed to assure continuous service. A machine room foreman believes the time between breakdowns of a particular electrical generator is best approximated by an exponential distribution with mean equal to 10 days.
a. What is the standard deviation of this exponential distribution?
b. Assuming that the foreman has correctly characterized the distribution for the time between breakdowns and that the generator broke down today, what is the probability that the generator will break down again within the next 14 days?
c. What is the probability that the generator will operate for more than 20 days without a breakdown?