A materials scientist is testing the tensile strength of a new high-performance ceramic fiber. A random sample of 12 fibers is tested, and the failure load, www kN, is recorded for each. The data are summarized as follows:
∑w=120,∑w2=1244 \sum w = 120, \quad \sum w^2 = 1244 ∑w=120,∑w2=1244You may assume that the failure loads are normally distributed.
Calculate a 95% confidence interval for: (i) the mean failure load of the ceramic fibers, (ii) the variance of the failure load of the ceramic fibers.
Fibers with a failure load of less than 8 kN are considered "substandard". Using the confidence limits derived in part (a), determine the lowest estimate for the proportion of fibers that are classified as substandard.
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.