The battery life, TTT minutes, of a 'Sky-Runner' delivery drone is normally distributed with mean 145 minutes and standard deviation 18 minutes.
Drones that last for more than 175 minutes are classified as having 'Extended Performance' status.
Determine the proportion of drones that achieve 'Extended Performance' status.
The manufacturer guarantees that the top 90% of drones will last at least kkk minutes.
Find the value of kkk.
Of the drones that achieve 'Extended Performance' status, the top 15\frac{1}{5}51 are classified as 'Ultra-Premium'.
Find the minimum battery life, sss, required for a drone to be classified as 'Ultra-Premium'.
A technician selects 3 drones at random from those that have achieved 'Extended Performance' status.
Find the exact probability that at least one of these drones is classified as 'Ultra-Premium'.
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.