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They cannot. Test scores are either marks or percentages based on marks (out of the total) and so are discrete.
There is no real relationship. Probabilities for the Normal distribution are extremely difficult to work out. The z-score is a method used to convert any Normal distribution into the Standard Normal distribution so that its probabilities can be looked up in tables easily. There are infinitely many types of continuous probability distributions and the Normal is just one of them.
Mountains are continuous.
It is continuous.
Continuous