The operational lifespan, in minutes, of high-performance lithium batteries for two different drone models follows normal distributions. Type Alpha batteries have a mean lifespan of 1250 minutes and a standard deviation of 45 minutes. Type Beta batteries have a mean lifespan of 1180 minutes and a standard deviation of 55 minutes.
One battery of each type is selected at random.
Determine the probability that the Type Alpha battery lasts longer than the Type Beta battery.
A fleet of drones is fitted with four Type Alpha and four Type Beta batteries, all operating independently.
Calculate the probability that the total combined lifespan of these eight batteries is greater than 9850 minutes.
