Men's shirt sizes are determined by their neck sizes. Suppose that men's neck 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
Neck size
S
145 neck size < 15
M
15 s neck size < 16
L
165 neck size <17
XL
17 5 neck size < 18
I
(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? Show your work.