Final answer:
The question is likely asking for the probability calculation related to the lifetime of components following an exponential distribution with a mean of 65 hours, a topic within Mathematics at the College level.
Step-by-step explanation:
The question likely pertains to the calculation of various probabilities involving exponential distribution, given that the mean lifetime of a component is 65 hours. The subject area this question falls under is Mathematics, specifically within the domain of probability and statistics, commonly studied at the college level. Exponential distribution is a continuous probability distribution that is widely used to model the time until an event occurs, such as the failure of an electronic component or the lifespan of products.
- What is the probability that a component fails within 10 hours?
- How long do 90% of the components last?
- If a component has already lasted 50 hours, what is the probability it will last an additional 30 hours or more?
These examples require an understanding of exponential distribution's properties, such as its memorylessness, which implies that the probability of an event occurring in the next time interval is independent of how much time has already passed.