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.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.