as any avid box reader knows cereal is sold by weight and no

as any avid box reader knows cereal is sold by weight and not volume. this introduces variability in the volume due to settling. as such, the height to which a cereal box is filled is random. if the heights for a certain type of cereal box have a normal (12,0.5) distribution in units of inches, what is the chance that a randomly chosen cereal box has a ceral height of 10.7 inches or less?

Solution

So the chance that a randomly chosen cereal box has a ceral height of 10.7 inches or less is

P(X<10.7) = P((X-mean)/s <(10.7-12)/0.5)

=P(Z<-2.6) = 0.0047 (from standard normal table)