Let X = x ~N : 1 x 19 and for some a, b R , Y = a x+b: x X . If the mean and variance of the elements of Y are 30 and 750, respectively, then the sum of all possible values of b is

Step-by-step solution

Mean of X = 1+19 2 = 10 , Variance of X = 19^2-1 12 = 30 . For Y = aX + b : Mean of Y = 10a + b = 30 and Variance of Y = a^2 30 = 750 . a^2 = 25 a = 5 or a = -5 . If a = 5 : b = 30 - 50 = -20 . If a = -5 : b = 30 + 50 = 80 . Sum of all possible values of b = -20 + 80 = 60 .