A safety engineer tests the breaking strength of steel cables. The manufacturer claims the cables have a mean breaking strength of 80 kN. The engineer suspects the cables are weaker than claimed. Data from 200 cables are summarized below:
n=200∑x=15940∑x2=1271162 n = 200 \quad \sum x = 15940 \quad \sum x^2 = 1271162 n=200∑x=15940∑x2=1271162Find the mean and standard deviation of the sample.
Carry out a hypothesis test to test the engineer's suspicion at the 1% significance level. State your assumptions clearly.
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.