Mean score: 78 ,standard deviation: 2.4, percent of scores in 75.6 and 85.2 range?

Question

I'm having trouble with this standard deviation problem, can someone explain it?

Answer 1

z = (x - μ)/σ

 

z = (85.2 - 78)/2.4 = 3   → area = .4987

 

z = (75.6 - 78)/2.4 = -1  → area = .1587

 

Add these areas → = .6574 = 65.74%

 

A²