The mass of a high-precision turbine blade is modelled by a normal distribution with a mean of 450.0450.0450.0 g and a standard deviation of 12.412.412.4 g. After a change in the manufacturing process, a quality control engineer suspects that the mean mass of the blades has decreased. A random sample of 505050 blades is measured, and the sample mean mass is found to be 446.2446.2446.2 g. Carry out a hypothesis test at the 2%2\%2% significance level to investigate the engineer's suspicion.
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.