Sample statistics such as sample mean and sample proportion are not fixed. Their values fluctuate from sample to sample.
Sample statistics are random variables that follow some probability distributions.
When we use a sample statistic to estimate the population parameter m , we don't expect that they are equal. To obtain an error bound, it's necessary to study the behavior of and, as a result, probability distribution. The CLT allows us to use normal probability distribution to answer probability questions about sample means , even though the population distribution of X is not normal. The number of accidents per week at a hazardous intersection varies with mean 2.2 and standard deviation 1.1. This distribution takes only whole-number values, so it is certainly not normal.