The weights of steers in a herd are distributed normally The

The weights of steers in a herd are distributed normally. The standard deviation is 100 lbs and the mean steer weight is 1300 lbs. Find the probability that the weight of a randomly selected steer is between 1169 and 1400 lbs.

Solution

We first get the z score for the two values. As z = (x - u) / s, then as          
x1 = lower bound =    1169      
x2 = upper bound =    1400      
u = mean =    1300      
          
s = standard deviation =    100      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    -1.31      
z2 = upper z score = (x2 - u) / s =    1      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.095097918      
P(z < z2) =    0.841344746      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.746246828   [answer]