A high-precision centrifuge is used in a chemical refinement process. The process involves two stages of separation.
The time, SSS minutes, taken to complete the first separation stage is modelled by a normal distribution with mean 112.5 minutes and standard deviation 14.8 minutes.
Use standardisation to find the proportion of cycles that take less than 135.0 minutes to complete the first separation stage.
Only the most efficient 12% of cycles (those with the shortest completion times) from the first separation stage are passed through to a second refinement stage.
Use standardisation to find the maximum time a cycle can take in the first separation stage if it is to be passed through to the second refinement stage.
The time, TTT minutes, for a cycle in the second refinement stage is modelled by a normal distribution with mean μ\muμ and standard deviation σ\sigmaσ.
Given that P(μ−10.4<T<μ+10.4)=0.82P(\mu - 10.4 < T < \mu + 10.4) = 0.82P(μ−10.4<T<μ+10.4)=0.82
Find P(T>μ−5.2∣T>μ−10.4)P(T > \mu - 5.2 \mid T > \mu - 10.4)P(T>μ−5.2∣T>μ−10.4)
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.