A civil engineer tests the load-bearing capacity of a new alloy beam. The design specification requires a mean breaking load of 80.0 kN.
The engineer suspects that the mean breaking load has decreased, and tests a random sample of 50 beams. The breaking loads, in kN, are denoted by xxx, and
∑x=3992.5\sum x = 3992.5∑x=3992.5 and ∑x2=318810.5\sum x^{2} = 318810.5∑x2=318810.5
Find the mean and the standard deviation of the breaking loads in the sample.
Stating your hypotheses clearly, test at the 1% significance level whether there is evidence that the mean breaking load is less than 80.0 kN. You may assume that the breaking loads are normally distributed with the standard deviation found in part (a).
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.