How large must [math]n[/math] be before [math]S_n = X_1 + X_2 +\cdots+ X_n[/math] is approximately normal? This number is often surprisingly small. Let us explore this question with a computer simulation. Choose [math]n[/math] numbers from [math][0,1][/math] with probability density [math]f(x)[/math], where [math]n = 3[/math], 6, 12, 20, and [math]f(x)[/math] is each of the densities in Exercise. Compute their sum [math]S_n[/math], repeat this experiment 1000 times, and make up a bar graph of 20 bars of the results. How large must [math]n[/math] be before you get a good fit?