The continuous flight time, T T\,T minutes, of a specific industrial drone model is normally distributed with a mean of 45.0 minutes and a standard deviation of 4.0 minutes.
Using standardisation, show that the probability that a randomly selected battery for this drone lasts less than 41.0 minutes is 0.1587.
A logistics company requires a drone to complete a survey flight that demands a battery flight time of at least 41.0 minutes. To qualify for the task, the operator has up to 3 batteries available to test. Batteries are tested sequentially; as soon as a battery lasts more than 41.0 minutes, it qualifies and testing stops.
Given that a drone successfully qualifies for the task within the 3 available attempts, and assuming flight times for all batteries are independent,
determine the probability that the drone qualified on the second battery tested with a flight time exceeding 53.0 minutes.