Assume that adults have IQ scores that are normally distribu

Assume that adults have IQ scores that are normally distributed with a mean of mu = 105 and a standard donation sigma = 20 Find the probability that a randomly selected adult has an IQ between 85 and 125.

Solution

We first get the z score for the two values. As z = (x - u) / s, then as          
x1 = lower bound =    85      
x2 = upper bound =    125      
u = mean =    105      
          
s = standard deviation =    20      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    -1      
z2 = upper z score = (x2 - u) / s =    1      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.158655254      
P(z < z2) =    0.841344746      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.682689492   [ANSWER]