In a test, students averaged 38.4 marks with a standard deviation of 12.5 marks.

a) Assuming that those test marks are known to be normally distributed, what is the probability that a given student will score less than 35 marks in the test?

b) Now, if test marks are not known to be normally distributed, what is the probability that a sample of 36 students will average less than 35 marks in the test?

c) Briefly explain why your answers in a) and b) are different.