Question

The Central Limit Theorem indicates that the sampling distribution is approximately normal. Why does this allow us to use the NORM.DIST and NORM.INV functions on TI-84 Plus calculator

Answer 1

Since the central limit theorem tells us that the sampling distribution is approximately normal assuming the conditions are met.

This means we can use the normal distribution to approximate and hence we can use a normal table to find out probabilities. And usually, we need this theorem to perform the z and t-tests.

Now NORM.DIST is just P(X < x) when X is a normally distributed random variable.

And the NORM.INV is just x for which probability is known. i.e. P(X < x) = k, then it gives out x.

These are the calculator approach for the same normal distribution table.