True or False 1 The central limit theorem always holds true

True or False?!

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

2-- According to the central limit theorem, the mean of the distribution of sample means will be the same as the original population mean.

3-- According to the central limit theorem, the standard deviation of the distribution of sample means will be the original population standard deviation divided by N (the sample size).

4-- The typical distance of a sample mean from the true population mean is measured by the standard error of the means.

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

Solution

1-- The central limit theorem always holds true, regardless of the sample size. FALSE

2-- According to the central limit theorem, the mean of the distribution of sample means will be the same as the original population mean. TRUE

3-- According to the central limit theorem, the standard deviation of the distribution of sample means will be the original population standard deviation divided by N (the sample size). FALSE

4-- The typical distance of a sample mean from the true population mean is measured by the standard error of the means. TRUE

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