The hydrostatic head (a measure of water resistance) of fabric treated with 'HydroGuard' is normally distributed with a standard deviation of 450 mm. A quality control check of 25 samples from Production Line X found a mean hydrostatic head of 3200 mm.
Determine a 98% confidence interval for the mean hydrostatic head of fabric from Production Line X.
An independent sample of 30 items from Production Line Y yielded a mean hydrostatic head of 3450 mm. An engineer suggests that the mean resistance of fabric from Line Y is higher than that of Line X.
By clearly stating your hypotheses, test the engineer's suggestion at the 1% level of significance.
The regulatory standard for this fabric is a mean hydrostatic head of μ\muμ mm. When looking at the two production lines individually, at the 1% significance level, there is insufficient evidence to conclude that the mean resistance of Line X is less than μ\muμ, and insufficient evidence to conclude that the mean resistance of Line Y is less than μ\muμ.
Calculate the maximum possible value of μ\muμ, giving your answer to the nearest integer.