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

1. Aurora finds a chart that says resting heart rates between $70$ and $79$ (inclusive) are considered average for women her age. What proportion of her peers should she expect to be 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. What portion of her classmates would she expect to be in excellent shape?

   Hint (b):

   normalcdf($-10^\wedge99, 66,$, mean, standard deviation)

3. Aurora’s fitness program lowers her resting heart rate by $4$ bpm. If every woman lowers her heart rate 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.