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(a) Consider the normal distribution with mean 6 and standard deviation 2. Find its population level first and third quartile using the qnorm function. Compute the population level inter-quartile range.

(b) Sample 100 observations from a Normal distribution with mean 6 and standard deviation 2, and report only the first and third quartile, and the inter-quartile range for your sample. Repeat this process for five times.

(c) Increase the number of observations to 100,000, and answer the same questions as in part (b).