In the search for a new quality-control specification for concrete more definitive than just a lower limit, a confidence-interval type of specification has been suggested. It is argued that if the 28-day strength of standard cylinders is to be well controlled, the specification should state that, say, 90 percent of the test results shall lie in a given range. Questions arise in the use of such a decision rule owing to limitations on sample size. For example, it is desired that the concrete have a mean strength of 4000 psi. Assume that concrete cylinder strengths are normally distributed and that the standard deviation is stable and known to equal 600 psi. The specification states that 90 percent of the test results must lie in the range 3000 to 5000 psi (i.e., about m ± 1.65σ). Unfortunately, the actual sample size may be as small as three. Assume that three strengths-3600, 4600, and 4400 psi-have been observed. Assuming a "perfectly vague" prior distribution on the mix mean, what is the probability that the true mean is equal to or greater than 4000 psi? If the true mean is in the range 3500 to 4500 psi, no significant loss is involved, but a loss of $1,000 is assumed if the true mean is below 3500 psi or above 4500 psi, and it is not reported. Compute the expected loss of accepting (based solely on the three observations) the mix as having a true mean in this range.