Put a lid on it! 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 snugly 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 “diameter” of between 3.95 and 4.05 inches.

The restaurant’s lid supplier claims that the diameter of their large lids follows a Normal distribution with mean 3.98 inches and standard deviation 0.02 inches.

Assume that the supplier’s 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 parts

(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?