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. According to this model, what percentage of women in the U.S. are under $4$ feet $11$ inches tall?

   Hint (a):

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

   Answer (a):

   normalcdf$(−10^\wedge 99, 59, 63.8, 2.7)$

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

   Step (b):

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

3. How many senior girls would you predict are taller than $6$ feet at North City High? What assumption(s) are you making?

   Hint (c):

   Follow the same steps you used in part (a).

4. Suppose you find out that North City High School is a private boarding school with a championship girl’s basketball program, and they recruit basketball players from across the state. Would your answer to part (c) change? Explain.

   Answer (d):

   It is likely that there will be girls over $6$ feet tall, and the senior girls are probably not a representative sample of women in the U.S.