Find the area of the shaded region under the given normal cu

Find the area of the shaded region under the given normal curve. mu = 4, sigma = 2. Use the table. The area of the region under the curve between x - 3 and x - 7 is

Solution

We first get the z score for the two values. As z = (x - u) / s, then as          
x1 = lower bound =    3      
x2 = upper bound =    7      
u = mean =    4      
          
s = standard deviation =    2      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    -0.5      
z2 = upper z score = (x2 - u) / s =    1.5      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.3085      
P(z < z2) =    0.9332      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.6247       [ANSWER]