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 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.