A laboratory centrifuge extracts rare-earth minerals from a solution. The mass of mineral extracted per batch, MMM grams, is modelled by a normal distribution with mean 828282 and standard deviation 6.56.56.5.
Find the probability that a randomly selected batch yields a mass greater than 959595 grams.
The extraction settings are modified, changing the mean to μ\muμ grams while keeping the standard deviation at 6.56.56.5 grams. Two independent batches are processed using these settings.
The probability that the mass extracted in both batches exceeds 909090 grams is 0.02250.02250.0225.
Find the value of μ\muμ, giving your answer to 1 decimal place.
In a separate test phase, the calibration is adjusted so that the mass extracted follows a normal distribution with mean 151515 and standard deviation 252525. Four independent batches are then processed.
Find the probability that at least one of these batches yields a negative mass reading.
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.