Answer
No surprise, see explanations below.
Work Step by Step
Given $\mu=1028,\sigma=100,n=200,\bar X=1050$
we should no be surprised that the sample mean is
not the same as the population mean since we do not
know the population distribution and this sample mean
is only from one sample of data.
The Central Limit Theorem states that as the sample size n increases without limit, the shape of the distribution of the sample means taken with replacement from a population will approach a normal distribution.
In this problem, the sample mean is from a particular sample, its mean is part of a normal distribution with a sampling mean equal to that of the population. It is of no surprise to have this sample mean differ from the sampling mean with a standard error of a normal distribution.
