The energy density of a new lithium-sulfur battery cell, measured in Wh/kg, is tested across two developmental stages.
In stage one, the energy density, DDD, is modeled by a normal distribution with a mean of 420 Wh/kg and a standard deviation of 25 Wh/kg.
Use standardisation to determine the proportion of battery cells produced in stage one that have an energy density of less than 460 Wh/kg.
Only the cells with the highest 25% of energy densities are selected for use in a premium range of electric aircraft.
Use standardisation to find the minimum energy density a cell must achieve in stage one to be selected for the premium range.
In stage two, the cycle life of the cells, LLL (measured in number of charge-discharge cycles), is modeled by a normal distribution with mean μ \mu\,μ and standard deviation σ\sigmaσ.
Given that P(μ−150<L<μ+150)=0.94P(\mu - 150 < L < \mu + 150) = 0.94P(μ−150<L<μ+150)=0.94
Find P(L>μ−75∣L>μ−150)P(L > \mu - 75 \mid L > \mu - 150)P(L>μ−75∣L>μ−150)
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.