We will test the idea that a Standard Normal random variable can be simulated by using the sum of n = 12 Uniform( 0, 1 ) random variables and subtracting 6. The mean of Uniform( 0, 1 ) is 1/2, and the variance is 1/12.
Thus the mean of the sum of 12 uniforms is 6, and the variance is 1. According to the Central Limit Theorem, the sum of 12 uniforms is approximately normally distributed.
Include a printout and mark ( circle or highlight) the answers.
a) Simulate S = 10,000 random samples of size n = 12 each from Uniform( 0, 1 ) distribution. For each of the s = 1 : 10,000 datasets, compute the sample total and subtract 6. Do NOT print the simulated values.
b) Compute the (sample) mean the 10,000 simulated values.
c) Compute the (sample) standard deviation the 10,000 simulated values.
d) Make a histogram for the 10,000 simulated values.
e) Make a Normal Q-Q plot for the 10,000 simulated values.
f) What proportion of the simulated values are greater than 1?