Which of the following statements about the sampling distribution of the mean (distribution of sample means) and the central limit theorem (CLT) are true? Select four (4) true statements from the list below: . If a population is perfectly normal, then for the distribution of sample means of any size, z= and z = The sampling distribution is always approximately normal even if the population is not normal. If the population is approximately normally distributed, then sample size does not matter for the central limit theorem to apply. The shape of the sampling distribution is closer to the population shape as the sample size increases. If and = then the distribution of sample means is normal. The smaller the sample size, the larger the difference between the mean of the sampling distribution and the population mean. From the same population, the mean of the sampling distribution () with n = 3 will be the same as the mean with n = 17. From the same population, the standard error of the sampling distribution with n = 16 will be the same as the standard error with n = 42. The sampling distribution of the mean will be approximately normal when or is large. The sampling distribution is still assumed to be approximately normal if the underlying population is non-normal as long as the sample size is large The smaller the sample size, the larger the standard error.