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.
390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.