True or False?!

1-- The central limit theorem always holds true, regardless ofthe sample size.

2-- According to the central limit theorem, the mean of thedistribution of sample means will be the same as the originalpopulation mean.

3-- According to the central limit theorem, the standarddeviation of the distribution of sample means will be the originalpopulation standard deviation divided by N (the samplesize).

4-- The typical distance of a sample mean from the truepopulation mean is measured by the standard error of themeans.

5-- If the original population has a bimodal distribution, thedistribution of sample means for that population, with N = 100 foreach sample, will also have a bimodal distribution.