The volume of coffee, VVV ml, dispensed by an automated brewing machine is normally distributed with a mean of 340 ml and a standard deviation of 15 ml. Servings containing more than 365 ml are categorized as 'Premium' servings.
Determine the proportion of servings categorized as 'Premium'.
The manufacturer wants to award a 'Standard' quality mark to the servings in the top 90%, which are those containing at least kkk ml. Find the value of kkk.
Within the 'Premium' category, the largest 15\frac{1}{5}51 of servings are further designated as 'Gold Reserve'. Find the minimum volume, sss, required for a 'Gold Reserve' designation.
A quality control officer randomly selects 5 servings that were already categorized as 'Premium'. Find the exact probability that at least one of these is a 'Gold Reserve' serving.
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.