A new roller coaster at an amusement park requires individuals to be at least 4' 8" (56 inches) tall to ride. It is estimated that the heights of 10-year-old boys are normally distributed with μ = 54.5 inches and σ = 4.5 inches.
a. What proportion of 10-year-old boys is tall enough to ride the coaster?
b. A smaller coaster has a height requirement of 50 inches to ride. What proportion of 10 year-old-boys is tall enough to ride this coaster?
c. What proportion of 10-year-old boys is tall enough to ride the coaster in part b but not tall enough to ride the coaster in part a?