In earlier class units, we saw that a dataset that included the mean values deri

In earlier class units, we saw that a dataset that
included the mean values derived from sampling
from a dataset with an unknown distribution could be
treated as a new random variable, and that this new
variable had several important properties.
Explain how collecting mean values (X-bar) from
samples drawn from a dataset, regardless of the
statistical distribution of the dataset, results in a
distribution of those values that is centered on the
mean value of the original dataset and is
approximately normally distributed depending upon
the sample size used. Include the name the theorem
that describes this phenomenon, and discuss what it
means to treat the X-bar data points derived from
sampling as a new random variable. Why is this
important in engineering?