The battery life durations of a specific model of commercial drone are known to follow a normal distribution with a mean of 48.5 minutes48.5\text{ minutes}48.5 minutes and a standard deviation of 3.2 minutes3.2\text{ minutes}3.2 minutes.
A drone of this model is selected at random for testing.
Find the probability that the battery life of this drone is less than 45.0 minutes45.0\text{ minutes}45.0 minutes.
The manufacturer classifies the top 12%12\%12% of these drones, in terms of battery life, as "High-Performance".
Estimate, to 2 decimal places, the minimum battery life a drone must have to be classified as "High-Performance".
228 exam-style questions on CCEA A Level Maths 4.5.1 Statistical distributions (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.