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 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.