5. (10 pts.] Removing outliers from a data set is a key preprocessing step when applying statistical technqiues in data science. The algorithm REMOVEOUTLIERS takes as input an array A of n numbers and a positive number c and outputs a sorted ordered list L of the numbers in A excluding outliers, where an outlier is defined as a number which deviates more than a factor c from its average u of the numbers in A, relative to the standndard deviation o of the numbers in A. It uses several auxiliary functions. The functions MEAN and STD both take as input an array of n numbers and output the average and standard deviation of those numbers, respectively. Assume that they both run in linear time and use a constant amount of space. The function FINDBETWEEN extract all the elements of an array A of n numbers that are larger than a given value x and smaller than another given value y, all given as input, and returns the elements in A that are in that range usig a sorted/ordered list data structure. Algorithm 3 REMOVEOUTLIERS(A,C) 1: U MEAN(A) 2: O + STD(A) 3: return FINDBETWEEN(A,u - C*0,4 +0*0) (a) Provide an efficient algorithm, in pseudcode, for the function FINDBETWEEN described above: complete the step-by-step by writing down the missing statements, already started for you below. Assume that you have available an implementation of the sorted- list ADT which includes the method INSERT which, taking as input an element, inserts the element in the proper position in the sorted list, and does so in linear time and constant space. (Make sure to use indentation to clearly indicate the proper scope of each statement.) Algorithm 4 FIND BETWEEN(A, x, y) 1: L new sorted list initially empty - a # 5: return L (b) Give the tightest/best possible time and space characterization, Big-Oh, Big-Theta, or Big-Omega, in terms of n, of the algorithm FINDBETWEEN. Justify your answer. Assume the implementation of the insert operation takes time linear in the size of the sorted list and uses a constant amount of space. (c) Give the tightest/best possible time and space characterization, Big-Oh, Big-Theta, or Big-Omega, in terms of n, of algorithm REMOVEOUTLIERS. Justify your answer. Assume the implementation of the insert operation takes time linear in the size of the sorted list and uses a constant amount of space