The mass of a high-precision turbine blade, M M\,M grams, is modeled by a normal distribution with a mean of 450.5 g and a standard deviation of 1.8 g. A quality control engineer selects a random sample of 20 blades from a large production batch. Determine the probability that the mean mass of these 20 blades, Mˉ\bar{M}Mˉ, is greater than 451.2 g.
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.