Under the normal curve, approximately what percent of scores fall between and - 1 to + 1 standard deviations around the mean?

According to the empirical rule, roughly 68% of the scores fall between z = - 1 and z = 1

You can use a calculator to get a more approximate answer. If you have a TI calculator, you can use the "normalcdf" function to type in normalcdf (-1,1)