A study in 1960 found that the average student spent an average of 24 hours studying a week with a standard deviation of 5.4 hours (call this random variable X). A more recent study found students spent an average of 14 hours studying a week with a standard deviation of 3.1 hours (call this random variable Y). X and Y are both normally distributed. Use the EMPIRICAL RULES only! to answer the following probabilities.

a) Find (18.6 34.8).

b) Find ( 20.2).

c) Given that a student in 1960 was known to study more than 18.6 hours a week, find the probability that this student studied more than 29.4 hours a week.

d) For the more recent study, find the value that determines the top 2.5% of weekly study hours of students.