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'.
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.