Question: Men's shirts are classified according to size as, \(\mathrm{S}, \mathrm{M}, \mathrm{L}, \mathrm{XL}\), corresponding respectively to neck circumferences of under 15 inches (for \(S\) ), between 15 and 16 inches (for \(\mathrm{M}\) ), between 16 and 17 inches (for \(\mathrm{L}\) ), and over 17 inches (for \(\mathrm{XL}\) ). Suppose that neck circumferences \(\mathrm{X}\) for adult males have a normal distribution with \(\mu=15.75\) and \(\sigma=0.70\)

1. How many shirts should be manufactured in each category of shirt size if 1000 shirts are to be manufactured?
2. If you wanted to define categories \(\mathrm{S}, \mathrm{M}, \mathrm{L}, \mathrm{XL}\) so that each category contained \(25 \%\) of the total population of adult males, what neck sizes would you assign to each of these categories?
   
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