Question 2 After recent events on earth, the European Space Agency are redoubling their efforts to establish a colony on Mars. Their plan is to send 40 different landing crafts. 3 (a) The perfect landing spots for each of the 40 landing crafts have been selected. However due to conditions on Mars, it is expected that when landing they may fall short of or overshoot their target landing spots, in which case their distance from the landing spot will be negative or positive respectively. From their simulations, the engineers estimate that the distribution of actual landing locations will follow normal distributions around the centres of the target locations, with a standard deviation of 300m. (i) Considering an individual landing craft, what is the probability that it will it will fall short of its landing spot by 100m or more? (ii) Considering an individual landing craft, what is the probability that it will land within 100m of the centre of its target location? (iii) What is the probability the average distance of all crafts from their centres will be less than 50m? (iv) The engineers would like to select a distance from the centres, from which they can have 99% confidence that all landers will land within. What is this distance? (15 marks)