Apologies for the lack of a descriptive title but I don't know well how to describe this problem. I received it during an online pre-interview test earlier this year for an algo trading role. I was unable to solve it from a probabilistic standpoint and have still been unsuccessful, only doing so by coding a quick MC simulation. Perhaps this was their goal given it was an algo-based position, but I can't help but feeling there is a simpler method. I don't know the exact figures from my question, but found an identical format online.
Two laptop manufacturing companies A and B are fierce rivals. A's laptops have a mean life of 4.9 years with a standard deviation of 1.2 years, while B's laptops have a mean life of 4 years with a standard deviation of 1 years. What is the probability that a random sample of 25 of A's laptops will have a mean life that is at least 1 year longer than that of a random sample of 49 of B's laptops?