A computer randomly generates scores (for a given population) between 0 and 100. (Uniform distribution) The mean of the scores in the population is therefore 50 with a standard deviation of 28.8675.

You draw all samples of size n = 50 from said population. For each sample you calculate the average of the scores. What is the distribution of averages in question called? What is its center of gravity? What is its standard deviation? What is its shape? Said distribution obeys which law and by virtue of which law / theorem?