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 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.