What Is Central Limit Theorem?
Central limit theorem states that as sample size (n) increases, the shape of the sampling distribution of the mean becomes closer to normal no matter what the shape of the distribution of the population.
The rule of thumb is when sample size is more than or equal to 30, the distribution will be relatively normal regardless of whether the underlying distribution is skewed or not
Hence, Z or T test can be used to standardised the scores even if the distribution is skewed as long as n is more than or equal to 30