Question: 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

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? SHOW YOUR WORKINGS.

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? SHOW YOUR WORKINGS.

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

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