Since, during a slip of the soil, small strengths in parts of a slope of generally homogeneous soil will be compensated for by larger strengths elsewhere, it has been suggested that the stability of the slope is related directly to the spatial average strength of the material. If the strength value (say, the shear strength) used in design is the observed mean divided by a safety factor, find the probability that the design value used will be less than the true mean if a sample size of three is used and safety factor = 1.5. Assume that the underlying variable X is normally distributed with unknown mean and variance.