Could something please explain question 3 a and 3 b in the S3 June 2010 paper:
3. A woodwork teacher measures the width, w mm, of a board. The measured width, X mm,is normally distributed with mean w mm and standard deviation 0.5 mm.
(a) Find the probability that X is within 0.6 mm of w.
The same board is measured 16 times and the results are recorded.
(b) Find the probability that the mean of these results is within 0.3mm of w.
The answers are: for a - 0.7698, for b - 0.9836.