3. A woodwork teacher measures the width, \(w \mathrm {~mm}\), of a board. The measured width, \(X \mathrm {~mm}\), is normally distributed with mean \(w \mathrm {~mm}\) and standard deviation 0.5 mm .
- Find the probability that \(X\) is within 0.6 mm of \(w\).
The same board is measured 16 times and the results are recorded.
- Find the probability that the mean of these results is within 0.3 mm of \(w\).
Given that the mean of these 16 measurements is 35.6 mm ,
- find a 98\% confidence interval for \(w\).