The continuous discharge times, T T\,T hours, of a specific model of industrial battery are assumed to be normally distributed with mean 450 hours and standard deviation 40 hours.
Find P(T>530)P(T > 530)P(T>530).
Given that the probability the battery lasts longer than k k\,k hours is exactly one-third of the probability it lasts less than k k\,k hours, find the value of k k\,k to one decimal place.
State the statistical name given to the value of k k\,k found in part (b).
A higher-capacity battery model has discharge times assumed to be normally distributed with mean 520 hours.
Given that the 12th percentile for this battery model is 484.5 hours,
find the standard deviation of the discharge time for this model.