The volumes of liquid in a batch of artisan coffee pods are modelled by a normal distribution with mean μ\muμ ml and standard deviation σ\sigmaσ ml. Data from the quality control lab indicates that 8% of the pods contain more than 42 ml of liquid, while 4% of the pods contain less than 35 ml.
Sketch a diagram to represent this information, illustrating the distribution of the volumes.
Show that μ=42−1.4051σ\mu = 42 - 1.4051\sigmaμ=42−1.4051σ.
Determine a second linear equation involving μ\muμ and σ\sigmaσ, and hence calculate the value of μ\muμ and the value of σ\sigmaσ to 2 decimal places.
Calculate the probability that a randomly selected pod from this batch contains more than 37 ml of liquid.
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.