The weights ot'chickcns for sale in a shop are normally distributed with mean 2.5 kg and standard deviation 11.3 kg. {a} A chicken is chosen at random. {i} Find the probability that it weighs less than 2 kg. {ii} Find the probability that it weighs more than 2.8 kg. {iii} Copy the diagram below. Shade the areas that represent the probabilities from parts {i} and (ii). {iii} Hence show that the probability that it weighs behireen 1 kg and 1.3 kg is 0.1935 [to four signicant gures}. {7} {b} A customer buys 10 chickens. {i} Find the probability that all It] chickens weigh between 2 kg and 2.8 kg {ii} Find the probability that at least 7 cf the chickens weigh between 2 kg and 1.8 kg. [5} [Total 13 marks]