In a large midwestern university 30 if the students live in

Solution

We first get the z score for the two values. As z = (x - u) / s, then as          
x1 = lower bound =    54.5      
x2 = upper bound =    70.5      
u = mean = np =    60      
          
s = standard deviation = sqrt(np(1-p)) =    6.480740698      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    -0.848668425      
z2 = upper z score = (x2 - u) / s =    1.620185175      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.19803291      
P(z < z2) =    0.947403747      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.749370837   [ANSWER]