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".
390 exam-style questions on OCR A Level Maths 2.4 Statistical Distributions, covering 2.4.1 Discrete probability distributions, 2.4.2 Binomial distribution as a model, 2.4.3 Calculating binomial probabilities, 2.4.4 Mean and variance of the binomial (A-level only), 2.4.5 Normal distribution as a model (A-level only), 2.4.6 Probabilities using the normal distribution (A-level only), 2.4.7 Links to histograms, mean and standard deviation (A-level only), and 2.4.8 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.