The electrical capacities of standard and long-range battery cells produced for high-performance drones are independently distributed.
The capacity of a standard cell, CsC_sCs, is normally distributed with mean 3200 mAh3200 \text{ mAh}3200 mAh and standard deviation 40 mAh40 \text{ mAh}40 mAh.
The capacity of a long-range cell, ClC_lCl, is normally distributed with mean 6000 mAh6000 \text{ mAh}6000 mAh and standard deviation 90 mAh90 \text{ mAh}90 mAh.
A random variable VVV is defined as the total capacity of three randomly selected standard cells minus the capacity of one randomly selected long-range cell.
V∼N(a,b)V \sim \text{N}(a, b)V∼N(a,b) where aaa and bbb are positive constants.
Determine the value of aaa and the value of bbb.
Calculate the probability that a randomly selected long-range cell has a capacity greater than 1.81.81.8 times the capacity of a single randomly selected standard cell.
A random sample of three standard cells is tested.
Find the probability that the capacity of the first cell in the sample is at least 25 mAh25 \text{ mAh}25 mAh more than the mean capacity of all three cells in the sample.