Standard and high-capacity batteries for search drones are independently tested at a facility.
The flight times of standard batteries, SSS, are normally distributed with mean 120 minutes and standard deviation 5 minutes.
The flight times of high-capacity batteries, HHH, are normally distributed with mean 230 minutes and standard deviation 8 minutes.
The random variable W W\,W represents the total flight time provided by 2 randomly selected standard batteries (used sequentially) minus the flight time of 1 randomly selected high-capacity battery.
W∼N(a,b)W \sim \text{N}(a, b)W∼N(a,b) where a a\,a and b b\,b are positive constants.
Find the value of a a\,a and the value of bbb.
Find the probability that a randomly chosen high-capacity battery lasts more than 1.85 times as long as a randomly chosen standard battery.
A random sample of 3 standard batteries is taken.
Find the probability that the flight time of the first standard battery in the sample is at least 3.5 minutes longer than the mean flight time of all 3 standard batteries in the sample.
