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.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.