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 (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.