1) Men's shirt sizes are determined by their neck sizes. Suppose that men's sizes are approximately normally distributed with mean 15.7 inches and standard deviation 0.7 inch. A retailer sells men's shirts in sizes S, M, L,
XL, where the shirt sizes are defined in the table below.
Shirt Size
S
M
L
XL
Neck Size
14 s neck size < 15
15 < neck size < 16
16 s neck size < 17
17 s neck size < 18
a) Because the retailer only stocks the sizes listed above, what proportion of customers will find that the retailer
does not carry any shirts in their sizes (less than 14 and more than 18)? Show your work.