The number of bedrooms (1:) per occupied private dwelling across Melbourne has the following distribution: (This table excludes dwellings with zero or an unspecied number of bedrooms and counts dwellings with more than 4 bedrooms as having only 4.) a) Calculate the mean and variance of the number of bedrooms in a dwelling selected uniformly at random. b) Calculate the mean and variance of the total number of bedrooms in 100 dwellings selected unifome at random. c) State the approximate distribution for the total number of bedrooms in 100 dwellings selected unifome 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