Find the area of the shaded region The graph to the right de

Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. The area of the shaded region is (Round to four decimal places as needed.)

Solution

We first get the z score for the two values. As z = (x - u) / s, then as          
x1 = lower bound =    80      
x2 = upper bound =    115      
u = mean =    100      
          
s = standard deviation =    15      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    -1.333333333      
z2 = upper z score = (x2 - u) / s =    1      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.09121122      
P(z < z2) =    0.841344746      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.750133526 = 0.7501 [ANSWER]