In designing a concrete mix to meet specified "minimum strength" (ultimate compressive stress) requirements, the American Concrete Institute Code requires that the mix be designed such that the mean strength resulting is 1.5 standard deviations above the specified strength. It has been shown experimentally that the coefficient of variation of concrete strength remains almost constant when the mean is varied by adjusting the proportions-e.g., water-to-content ratio-of the mix design. Find an expression for the required mean strength (the value the mix designer uses) in terms of the specified strength S and the coefficient of variation V. The value of the coefficient of variation depends on the material quality, the working conditions, and the contractor's mixing and pouring policies. All else being equal, it serves as a measure of the latter, i.e., of the contractor's quality control, and usually remains constant from job to job. V may be as high as 20 percent for some contractors, as low as 10 percent for others. What reduction in (mean) mix design strength-and hence in material costs-can a contractor providing 5000 psi concrete (minimum specified strength) achieve if he is willing to allocate more time and men (to provide better treatment, placing, and curing of the concrete) sufficient to reduce the coefficient of variation from its present value of 15 to 10 percent? Sketch rough bell-shaped curves for the two conditions.