Aurora is starting a fitness program at her school and needs to find an easy measure of fitness to assign workouts and gauge improvement. She decides that using resting heart rate would be helpful. Assume that the resting heart rate of young women is approximately normally distributed with a mean of $74$ beats per minute (bpm) with a standard deviation of $5$ bpm.

1. Aurora found a chart that said resting heart rates between $70$ and $79$ (inclusive) are considered average for women her age. What proportion of her classmates would she expect to find in the average range?

   Hint (a):

   normalcdf($70$, $79$, mean, standard deviation)

2. The chart also claims that resting heart rate of $66$ or less indicates excellent fitness in otherwise healthy young women. What portion of her classmates would she expect to find in excellent shape?

   Hint (b):

   normalcdf($-10$^$99$, $66$, mean, standard deviation)

3. If Aurora’s fitness program lowers the mean heart rate of her female classmates by $4$ bpm, what will be the increase in the proportion of women now classified as being in excellent shape?

   Hint (c):

   What would the new mean be?
   Repeat your steps in part (b) with the new mean.