Can someone explain how the standard error range was determine and how 68% expected was determined?

Question

I understand the other aspects just not how the range from 2.52 to 3.68 was achieved, and a 68% expected.

Thank you

Answer 1

The area underneath the curve between the two outermost dashed lines is about $68\%$ of the area underneath the entire curve.

You'll also find it helpful to remember the 68-95-99.7 rule, which reminds you that $1,2,3$ standard deviations from the mean consume about $68\%, 95\%, 99.7\%$ of the area under the normal distribution.