A farmer finds the mean mass for a random sample of 200 eggs laid by his hens to be 57.2 grams. If the masses of eggs for this breed of hen are normally distributed with standard deviation 1.5 grams, estimate the mean mass, to the nearest tenth of a gram, of the eggs for this breed using a 99% confidence interval. (Recall the following Z-scores for each level of confidence: 90% = 1.645, 95% = 1.960, and 99% = 2.575.)

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