If your text book says "using the transformation $\displaystyle u_i= \frac{x_i- a}{b}$" then your text book will have to say what "a" and "b" mean- otherwise that is meaningless. I suspect that at least a clue follows the last item you give: it says the standard deviation of x is b times the standard deviation of u. What does your text book say about the standard deviation of u that makes that a useful transformation?