Statistics · Mean and variance of transformed data

Let

X = \{x \in \mathbb{N} : 1 \le x \le 19\}

and for some

a, b \in \mathbb{R}

Y = \{ax + b : x \in 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

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