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".
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.