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.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.