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.
