Question: Men's shirts are classified according to size as, \(\mathbf{S}, \mathbf{M}, \mathrm{L}, \mathrm{XL}\), corresponding respectively to neck circumferences of under 15 inches (for \(\mathbf{S})\), between 15 and 16 inches (for \(\mathrm{M})\), between 16 and 17 inches (for \(\mathrm{L}\) ), and over 17 inches (for XL). Suppose that neck circumferences \(X\) 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 \(\mathbf{S}, \mathbf{M}, \mathrm{L}, \mathrm{XL}\) 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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