The flight duration, LLL minutes, of a specific model of industrial drone follows a normal distribution with mean 54 and standard deviation 6.
A delivery company uses a fleet of 5 drones for a single mission. Find the probability that the total flight duration of these 5 drones exceeds 285 minutes.
The manufacturer wants to establish a "low battery" warning time ttt such that the probability of a drone's flight duration being less than ttt is 0.025. Determine the value of ttt.
To improve efficiency, a lightweight chassis is introduced. A random sample of 40 drones with the new chassis is tested, and their mean flight duration is found to be 56.3 minutes. Assuming the standard deviation remains 6, test, at the 1% level of significance, whether there is evidence that the mean flight duration has increased. State your hypotheses clearly.