Describe how the variability of the x bar distribution changes as the sample size increases

As we increase the sample size, the variability of the x bar distribution will follow a normal distribution (i.e. bell shape curve). The more independent random variables we add to the population, the more it will correspond or approach to the population mean (proximity) thereby clustering the distribution towards the center (mean). This is the essence of central limit theorem. 

Period is the time it takes for one “cycle” to complete. in the parent sine function, period is 2*pi since sin(0) = 0, sin(pi/2) = 1, sin(pi) = 0, sin(3pi/2) = -1, and sin(2pi) = 0. at that point, the sequence repeats itself. i’m not sure if your graph is similar to the sine function since you didn’t provide a picture, but you can find the period by looking at a graph.