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.
