The Central Limit Theorem does not specify what is meant by "a sufficiently large sample." What factor(s) about the population of values do you think determine how large is large enough for the approximate normal shape to hold?
Consider the California Decco example. Do you think n = 30 would be large enough for the distribution of possible values for the average loss to be approximately normal? Why or why not? Now consider the handspan measurements of females.
Do you think n = 30 would be large enough for the approximate normal shape to hold? What is different about these two examples?