According to the National Health Center, the heights of 5 year-old boys are Normally distributed with a mean of 43 inches and a standard deviation of 1.5 inches.

a. In which percentile is a 5-year-old boy who is 46.5 inches tall?

b. If a 5-year-old boy who is 46.5 inches tall grows up to be a man at the same percentile of height, what height will he be? Assume adult men’s heights (inches) are distributed as N (69, 3).