The mass of a high-precision turbine blade, in grams, is modelled by a normal distribution with mean 450.0 g and standard deviation 12.4 g.
After a change to the manufacturing process, a quality control engineer suspects that the mean mass of the blades has decreased. A random sample of 50 blades is measured and the sample mean mass is found to be 446.2 g.
Stating your hypotheses clearly, carry out a test at the 2% significance level to investigate the engineer's suspicion. You may assume that the standard deviation is still 12.4 g.
State one assumption, other than the value of the standard deviation, that the engineer has made in carrying out this test.
390 exam-style questions on OCR A Level Maths 2.4 Statistical Distributions, covering 2.4.1 Discrete probability distributions, 2.4.2 Binomial distribution as a model, 2.4.3 Calculating binomial probabilities, 2.4.4 Mean and variance of the binomial (A-level only), 2.4.5 Normal distribution as a model (A-level only), 2.4.6 Probabilities using the normal distribution (A-level only), 2.4.7 Links to histograms, mean and standard deviation (A-level only), and 2.4.8 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.