Reword the following answer: When we are using the t distribution for interval estimation, and especially when the sample size is very small, we usually make the assumption that the population from which the samples are derived is approximately normal. This is because the t distribution is a theoretical distribution that was derived under the assumption of population normality. When the distribution of the population is unknown or not normal, and the sample size is small, the usual z-score confidence interval formula (x +/- z(s/n)) might not provide accurate results because it is derived under the assumption of normally distributed populations and larger sample sizes. In these situations, the t distribution is preferable because it is more adaptable to smaller sample sizes and potential non-normality, compared to the z distribution which is predicated on larger sample sizes and the central limit theorem. So, the correct statement is "the population is approximately normal". It should be noted that the t distribution approach will still give reasonable results if the population is not exactly normal, but it is grossly non-normal distributions that can cause substantial inaccuracies. The assumpitons you listed are clarified below: 1. "The sample has a mean of at least 30": This does not have conceptual sense. 30 is typically referred to in terms of sample size, not the mean of the sample. 2. "The sampling distribution is not normal": If our sample size is large enough, we can apply the central limit theorem and assume the sampling distribution is normal regardless