Antelopes, native to Africa and Asia, range in size from 30 cm to over 180 cm at the shoulder, with most between 90-120 cm. This is related to the humerus length. The data below gives the length and mid-shaft diameters of the humerus bones of African Antelopes. Diameter 17.6 26 31.9 38.9 45.8 51.2 58.1 64.7 66.7 80.8 (mm) Length (mm) 82.9 161.7 203.5 240.0 267.9 300.0 319.7 348.9 383.8 387.3 436.8 447.1 a) Find the best model for humerus length based on mid-shaft diameter for African Antelopes. Provide all plots and necessary working. b) If an antelope has a mid-shaft diameter of 60 mm, what is the predicted humerus length? c) If an antelope has a humerus length of 550 mm, what would be the likely mid-shaft diameter? Are there any issues with this calculation? Question 6 [10 Marks] A magician performs the following card trick. She asks a volunteer to secretly select a number between 1 and 10 and deal out that many cards from a well-shuffled deck of 52 standard playing cards. The last card dealt determines a new number of cards to be dealt from those remaining: if it is an ace, the new number is 1; if it is Jack, Queen or King, the new number is 5; otherwise the new number is the face value of the card. The process is repeated until there are not enough cards left in the deck to continue. The magician then identifies the last card selected. The trick is that the magician repeats the process starting with the number 1. This will usually (but not always) result in selecting the correct final card, no matter what number the volunteer originally selected. a) Perform an experiment to estimate the probability the magician and the volunteer end up with the same final card. Give full details of the experiment and result. b) What is the population you are sampling in this experiment? c) Explain why the magician and volunteer are likely to end up with the same card, no matter what number the volunteer chooses initially.