At some fast-food restaurants, customers who want a lid for their drinks get
them from a large stack left near straws, napkins, and condiments. The lids
are made with a small amount of flexibility so they can be stretched across
the mouth of the cup and then snuggly secured. When lids are too small or too
large, customers can get very frustrated, especially if they end up spilling
their drinks. At one particular restaurant, large drink cups require lids with
a 鈥渄iameter鈥 of between 3.95 and 4.05 inches. The restaurant鈥檚 lid supplier
claims that the mean diameter of their large lids is 3.98 inches with a
standard deviation of 0.02 inches. Assume that the supplier鈥檚 claim is true.
(a) What percent of large lids are too small to fit? Show your method.
(b) What percent of large lids are too big to fit? Show your method.
(c) Compare your answers to (a) and (b). Does it make sense for the lid
manufacturer to try to make one of these values larger than the other? Why or
why not?