According to the National Health Statistics Report, the average height of adult women in the U.S. is $63.8$ inches with a standard deviation of $2.7$ inches. Heights can be modeled with a normal probability density function.

1. What percent of women are under $4$ ft $11$ in. tall?

   Hint (a):

   First, note that $4$ ft $11$ in. must be converted to inches.

   Step (a):

   normalcdf$(-10$^$99, 59, 63.8, 2.7)$

2. Most girls reach their adult height by their senior year in high school. In North City High School’s class of $324$ senior students, how many girls would you expect to be shorter than $4$ ft $11$ in.? (Note: Assume half of the senior students are girls.)

   Hint (b):

   Multiply $162$ by the percentage found in part (a).

   Answer (b):

   $≈ 6$

3. How many senior girls do you expect to be taller than $6$ ft at North City High?

   Hint (c):

   Follow the same steps you used in parts (a) and (b).