Question 1 (a) A mortar is about to fire on a road which is 20 metres wide and runs perpendicular to the line of fire. The standard deviation for errors in

range is 13 metres, while errors in line can be neglected. (i) The mean point of impact of the mortar is on the nearside edge of the road. Calculate the probability that a single shot hits the road. [2] (ii) If the mortar fires 3 shots, find the probability that at least two shots hit the road. [3] (iii) How many shots would the mortar need to fire in order to have a probability of at least 99% of hitting the road at least once? [3] (iv) State any assumptions you have made in these calculations and comment on their appropriateness or otherwise. [2] (b) A commander is worried that soldiers have become excessively dependent on gadgets and so organises a series of field trials to assess how well junior officers perform basic tasks. In one of these, 20 junior officers are asked to estimate the distance to a tree, where the distance is in fact exactly 53m. Their estimates have a mean of 50.1m with standard deviation 5.7m. (i) State appropriate hypotheses and hence test at the 5% level whether there is any evidence that junior officers are systematically either underestimating or overestimating the distance. [6] (ii) State any assumptions you have made in these calculations and comment on their appropriateness or otherwise. [2] (iii) Explain the concepts of type I and type II errors in the context of this test. [2]