4) A professor conducted a study on the sleep habits of her students. She found that their nightly sleep duration follows a normal distribution with an average of 7 hours and a standard deviation of 1.5 hours. (a) What is the probability of a student randomly chosen from the class getting less than 5 hours of sleep on a given night? (b) What percentage of students get between 6 and 8 hours of sleep? (c) If the professor wants to offer extra help sessions for students who chronically sleep less than 6 hours, what percentage of the class would be eligible? (Hint: Convert the desired values to Z-scores and use standard normal table to find the probabilities.)