A random sample of 64 breaking loads, in kN, gives ∑x=5203.2\sum x=5203.2∑x=5203.2 and ∑x2=424595.16\sum x^2=424595.16∑x2=424595.16. The design value for the population mean breaking load is 82 kN. An engineer believes that the population mean may be lower.
Calculate the sample mean and sample standard deviation.
Using a Normal approximation for the sample mean and the sample standard deviation as an estimate, test the engineer's belief at the 5% significance level.
390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.