An architect and engineer team up to design a new housing subdivision. The engineer proposes that they build homes in the shape of a cube to maximise internal volume while minimising materials used for the surface area (floor, walls and roof}. The architect is concerned every house will look identical so proposes that they vary the side length of the houses, x, by selecting lengths from a uniform distribution between 5 and 11m. Sketch the probability density function and then answer the following question: What is the probability a randomly selected house will have a side length greater than i'm? Enter your answer as a decimal value accurate to two decimal places, rounding as appropriate. e.g. if the probability was 23.5% you would enter a value of 0.24 in the answer space. If the probability was 1 in 4, you would enter a value of 0.25 An architect and engineer team up to design a new housing subdivision. The engineer proposes that they build homes in the shape of a cube to maximise internal volume while minimising materials used for the surface area (floor, walls and roof]. The architect is concerned everv house will look identical so proposes that they var'l:r the side length of the houses, x, by selecting lengths from a uniform distribution between 5 and 12m. What is the expected value for the volume of a house? Enter your answer assuming units of cubic metres rounding to the nearest whole number