The time taken to fully charge the high-capacity battery of a specialized cargo drone follows a normal distribution with a mean of 140 minutes140\text{ minutes}140 minutes and a standard deviation of 12 minutes12\text{ minutes}12 minutes.
Determine the probability that a randomly selected battery charge takes longer than 155 minutes155\text{ minutes}155 minutes.
Any battery charge that takes longer than 155 minutes155\text{ minutes}155 minutes is classified as an "extended duration" charge.
A drone's battery charge is monitored at random. Given that it is classified as an extended duration charge,
calculate the probability that the charge takes longer than 165 minutes165\text{ minutes}165 minutes.
Among the extended duration charges, exactly 15%15\%15% last longer than m minutesm\text{ minutes}m minutes.
Find the value of mmm.
