Standard Deviation and "False Alarm" Rate

Hello. I am a stats novice and have a question regarding how the
percentages quoated in the following statement were derived:

"It is important to note that even when there is no significant
difference between a student's score and the class average, tehse two
values will still differ by 0.5 or more standard deviations 35 percent
of the time, and by 1 or more standard deviations 24 percent of the
time. This represents a high percentage of "false alarms," which can
lead to inaccurate conclusions."

No additional information is provided. I am trying to determine how to
derive the 35% and 24% quoted above. Any assistance you can provide
would be greatly appreciated! Thank you!

.