Hi can you please help me with some basic questions? I'm self-teaching and I want to make sure I'm not messing up!

1. When you have the sampling distribution of the mean of any distribution, by applying the central limit theory you can calculate the standard error by sigma (or estimated sigma, if you don't know sigma) by the root of the # of your observations. When you keep your sample size the same and increase the number of trials, you approach a normal distribution with a smaller and smaller SD of the mean. If your sample size is 1 you don't get a nice bell shape for the mean sample size though if your population is not bell-shaped. Like when you have a sample of 1 you're just going to get closer and closer to the actual distribution. Is what I wrote right?

2. If your population is not bell-shaped (let's say very positively skewed), what minimum sample size do you need to get a bell-shaped distribution of the sample mean? Can it be as small as 2 as long as you have A LOT of simulations (a million, 5 million, 10 million, maybe more)?