Write a c++ program that reads a list of real numbers representing numeric scores, stores them into a vector, calls the function to calculate their mean and standard deviation, and then calls another function to display the letter grade corresponding to each numeric score

The sample of this program might looks like the following picture:

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Please input a list of students scores: 45 23 67 12 87 34 56 76

45 23 67 12 87 34 56 76

The man of number is 50

The variance of number is 604

The standard deviation of number is 24.6

student 1 score is C

student 2 score is D

student 3 score is B

student4 score is F

student5 score is A

student6 score is D

student7 score is C

student8 score is B

If x denotes the mean of a sequence of numbers x1, X2, of the deviations of the numbers from the mearn, xn, the variance is the average of the squares variance = (x1-4) 2 xi-xi - And the standard deviation is the square root of the variance, write functions to calculate the mean, variance, and standard deviation of the values stored in a vector and a driver to test your functions. Problem 2 Letter grades are sometimes assigned numeric score by using the grading system commonly called grading on a curve. In this scheme, a letter grade is assigned to a numeric score according to the following table, where m is the mean score and (sigma) is the standard deviation. X Numeric Score Letter Grade 3 3