what is the probiotic of randomly picking children that scor

Solution

We first get the z score for the two values. As z = (x - u) / s, then as          
x1 = lower bound =    55      
x2 = upper bound =    100      
u = mean =    75      
          
s = standard deviation =    11      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    -1.818181818      
z2 = upper z score = (x2 - u) / s =    2.272727273      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.034518174      
P(z < z2) =    0.98847869      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.953960516   [ANSWER]