The number of bedrooms (X) per occupied private dwelling across San Diego has the following distribution: Count __ __ __ __ u_ __ (This table excludes dwellings with zero or an unspecified number of bedrooms and counts dwellings with more than 4 bedrooms as having only 4.) a) Calculate the mean and variance ofthe number of bedrooms in a dwelling selected uniformly at random. b) Calculate the mean and variance ofthe total number of bedrooms in 100 dwellings selected uniformly at random. c) State the approximate distribution for the total number of bedrooms in 100 dwellings selected uniformly at random. On what theoretical basis can this approximation be made? d) Given 100 dwellings selected uniformly at random, what are the approximate probabilities these contain: i. more than 300 bedrooms in total, and ii. between 200 and 300 bedrooms in total