For females aged 18-24, systolic blood pressures (in mm Hg) are normally distributed with a mean of 114.8 and a standard deviation of 13.1.
a. If a woman between the ages of 18 and 24 is randomly selected, find the probability that her systolic blood pressure is above 120.
b. If 12 women in that age bracket are randomly selected, find the probability that their mean systolic blood pressure is greater than 120.
c. Given that part (b) involves a sample size that is not larger than 30, why can the central limit theorem be used?