The times spent studying by students in the week before final exams follows a normal distribution with standard deviation 8 hours. A random sample of four students was taken in order to estimate the mean study time for the population of all students.
a) What is the probability that the sample mean exceeds the population mean by more than 2 hours?
b) What is the probability that the sample mean is more than 3 hours below the population mean?
c) What is the probability that the sample mean differs from the population mean by more than 4 hours?
d) Suppose that a second independent random sample of 10 students was taken. Without doing the calculations, state whether the probabilities in parts (a), (b), and (c) would be higher, lower, or the same for the second sample.