your class average on a test was a 70 with a standard deviation of 3 points.What percent of the class fell between 67 and 76 points

your class average on a test was a 70 with a standard deviation of 3 points.What percent of the class fell between 67 and 76 points 

 

I am going to split this into 2 parts.  Below the mean and above the mean.

70-3=67           so 67 is one standard deviation below the mean

between -1 and +1 SD  from the mean lie 64% of all scores.  Half of this is 34%

 

70+2*3=76      and 76 is 2 standard deviations above the mean.

between -2 and +2 SD  from the mean lie 95% of all scores.  Half of this is 47.5%

 

Total prob of lying in desired region = 34+47.5 = 81.5%    approximately.