The continuous discharge times, T T\,T hours, of a specific model of industrial battery are assumed to be normally distributed with mean 450 hours and standard deviation 40 hours.
Find P(T>530)P(T > 530)P(T>530).
Given that the probability the battery lasts longer than k k\,k hours is exactly one-third of the probability it lasts less than k k\,k hours, find the value of k k\,k to one decimal place.
State the statistical name given to the value of k k\,k found in part (b).
A higher-capacity battery model has discharge times assumed to be normally distributed with mean 520 hours.
Given that the 12th percentile for this battery model is 484.5 hours,
find the standard deviation of the discharge time for this model.
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.