Central Limit Theorem

Question 1

What does the CLT show

Answer 1

The standardised sample mean of a sequence of iid random variables has a limiting standard normal distribution.
The standardised sample mean converges in distribution to the standard normal model. The theorem is valid regardless of the distribution of the X s

Question 2

How big should n be to use the CLT -

Answer 2

Theorem does not say how fast the convergence is. Usually

n ≈ 60 gives a good approximation

Question 3

What does the CLT tell us about sums of IID RVS

Answer 3

Any sum of IID RVs is approximately Gaussian

Question 4

If question about probabilities says is something within this…. what is it important to incorporate

Answer 4

absolute value - as could be plus or minus value if it has to be within a certain measurement