A large population has 45% men, 50% women and 5% non-binary people Research on the population has found that 40% of men. 70% of women and 60% of non-binary people help with the housework in their domestic household (a) One person is chosen from this population at random What is the probability that the chosen person helps with the housework? (4 marks] (b) One person is chosen from this population at random What is the probability that the chosen person is neither a man nor helps with the housework? [4 marks] (c) 7 person are chosen from this population at random What is the probability that at least 2 of the chosen people are men? [5 marks] (d) 1100 person are chosen from this population at random A scientist decides to modeli the number of men in this sample with N(495,272.25) First, justify the scientist's choice of 495 and 272.25 Then, use the model to calculate the probability that there are at least 479 men in the sample. [8 marks] (e) Ten samples of ten people were drawn from the population at random The number of people in each sample who helped with the homework is (4.5,5,5,5,6,7,7,7,9) What is the sample mean, sample median and sample standard deviation? Remember to give full workings. (4 marks]