Assume that the total score from both teams for college foot

Assume that the total score (from both teams) for college football games averages µ = 42 points per game, and that the distribution of total points is approximately normal with = 20.
What proportion of college football games have a point total between 20 and 60?

Solution

We first get the z score for the two values. As z = (x - u) / s, then as          
x1 = lower bound =    20      
x2 = upper bound =    60      
u = mean =    42      
          
s = standard deviation =    20      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    -1.1      
z2 = upper z score = (x2 - u) / s =    0.9      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.135666061      
P(z < z2) =    0.815939875      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.680273814   [ANSWER]