Question: Over the past 10 years, the local school district has measured physical fitness for all high school freshmen. During that time, the average score on a treadmill endurance task has been \(\mu \) = 19.8 minutes with a standard deviation of \(\sigma \) = 7.2 minutes. Assuming that the distribution is approximately normal, find each of the following probabilities.

a. What is the probability of randomly selecting a student with a treadmill time greater than 25 minutes? In symbols, p(X > 25) =?

b. What is the probability of randomly selecting a student with a time greater than 30 minutes? In symbols, p(X > 30) =?

c. If the school required a minimum time of 10 minutes for students to pass the physical education course, what proportion of the freshmen would fail?