9. A machine manufactures a large number of nails. The length, L mm, of a nail is normally distributed, where L - N(4, 3.5'). There are 12% of the nails which are longer than 59.2 mm , and they are classified as long nails. (a) Find the value of u. [4] There are three different types of classifications for the nails, based on their lengths. The following table shows the percentages and the weights of each classification: Classification Short Medium Long Percentage 55% 33% 12% Weight of a nail 0.8 g 1.1g 1.4 g A nail is classified as short if it is shorter than q cm. (b) Find the value of q. [3] (c) 10 nails are randomly selected. Let X be the number of short nails in this sample. (i) Find E(X). (ii) Find the probability that more than 5 of these nails are short. [6] All short and medium nails, in total m nails, are selected. It is given that the total weight of the nail is 949 kg. (d) Find the value of m. [41