Using R, generate a random sample of size n=10 from the following Normal Distribution: N ( = 100, 2 = 25). a) (1 pt) Use R to find the sample mean X, and sample variance s2. Show your output. b) (1 pt) Assume that the true variance is unknown. Using the sample variance, generate a 95% confidence interval for . c) (2 pts) Generate 500 independent samples of size n=10 from the same Normal distribution above. Use each of these samples to generate a 95% confidence interval for . (you will generate 500 different intervals) How many of your confidence intervals captured the true parameter value for ? Show your code and final output (answer) for this step. (You do not need to output all the confidence intervals)