A manufacturing plant produces steel rods. During one production run of 20,000 such rods, the specifications called for rods that were 46 centimeters in length and 3.8 centimeters in width. Fifteen of these rods comprising a random sample were measured for length; the resulting measurements are shown here. Use these data to estimate the population variance of length for the rods. Assume rod length is normally distributed in the population. Construct a 99% confidence interval. Discuss the ramifications of theresults.

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44 cm 45 cm 48 cm 47 cm 43 cm 48 cm 43 cm46 cm 44 cm 46 cm 46 cm 45 cm 47 cm 43 cm44 cm