Problem 4: Combinations of Normal DistributionsAssigned: 13 OctoberDue: 28 OctoberMaximum Mark: 10 PointsMaximum Submission Length: 3 pagesSuppose that a distribution is normal, with mean µ=10 and standard deviation s=5. Twosamples a and b, each of length N, are independently drawn from this distribution. Forwhich of the following operations on a and b will the resulting distribution also be normal?If the distribution is normal, state this and provide exact mathematical expressions (integer,fraction, radical, etc.) for the mean, median, and standard deviation of the new distribution(do not use a decimal). If the distribution is not normal, use R to numerically estimate thevalues and express the result as a decimal (at least 3 significant figures).Summarize your results in a table similar to the one given below. (Note that some quantitiesmay not be well-defined mathematically. You do not have to check for this, but you canmark possible cases with asterisks.) normal?MeanMedianStandard Deviationayes10105byes10105 a+3a+aa+ba-ba´ba/3|a-10|a+2ba2+b2a2-b2

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