4. The pass mark for EGA118 is 70. The problem is that the exam system expects a pass mark of 40. This means that the module marks have to be mapped to the exam system marks. The mapping uses linear equations as follows: If a student's module mark is 70 or less, all component marks are multiplied by a scaling factor equal to 4/7. If a student's module mark is above 70, all component marks are multiplied by the scaling factor equal to (2-100/MM). i. MM is the module mark. After multiplication all marks are rounded to the nearest integer. The module mark is equal to the sum of: The mark for the flight simulator exercise. This mark is out of 10 for the first attempt and capped to a maximum of 7 for the make-up quiz. The sum of the marks for the five Canvas quizzes. Each quiz is marked out of 2 for the first attempt and capped to 1.4 for the make-up quizzes. The sum of the marks for the seven presentations. The team gets up to 1 mark for each of the seven sets of slides and the presenter is marked out of 3. The sum of M1 + (M2 + M3)/10. M1 is the mark for the MATLAB quiz, which is out of 4 for the first sit and capped to 2.8 for the make-up quiz. M2 and M3 are the marks for the second and third MATLAB assignments, which are respectively marked out of 60 and 100. The exam contributes 25 % of the module mark. The exam has 50 marks available so the contribution to the final module mark is half the mark achieved. The problem solving exercise also contributes 25 % of the module mark. The exercise has 50 marks available so the contribution to the final module mark is half the mark achieved. As an example, assume a student scored 6 of the first attempt of the flight simulator quiz. In the make-up quiz they managed to achieve 8. As the make-up mark is capped this means they get 7 for the exercise. In the quizzes they passed all at the first attempt with marks of 1.8, 1.6, 2, 1.6, 1.4, which sum to 8.4. Their group marks for the slides were 0.9, 0, 0.8, 0.95, 0.85, 1, 0.9 and their individual presentation mark was 2.7. This makes the total presentation mark equal to 8.1. In the MATLAB they scored 3, 43, 64 marks, which gives a total of 13.7. In the exam they achieve 37 marks and in the problem solving exercise their mark was 28. This makes their total mark equal to: 7+ 8.4 +8.1 +13.7 + 0.5*37 + 0.5*28 = 69.7 This total is under 70 so their marks will be multiplied by 4/7. In this case the student will ultimately pass the module, final marks are always integer values and their unscaled mark is a pass when rounded to the nearest integer. For this question write a function that has a vector containing the six component marks, as contained in the bulleted list above and in the same order, as its input argument. The function should return the scaling factor that would be used in mapping between the module marks and the exam system mark. The function should check that the user has passed a vector with a length of six into it, if not the value returned should be set to -1. The function should also test that the values in the vector are valid, 0 to 10 for each of the flight sim exercise, presentations and quizzes, 0 to 20 for MATLAB and 0 to 25 for both the exam and problem solving exercise. Return the number -2 if any entry is outside the range. You do not need to test that the entries in the vector are all numbers, that can be assumed. Also write a script, in a separate file, that shows how you have tested your function. [20 Marks]