The Marvin Window Company estimated that the distribution of

The Marvin Window Company estimated that the distribution of the time for two construction workers to install 50 custom window sets is normally distributed with a mean of 32 hours and a standard deviation of 2 hours. What percent of 50 window sets take between 32 and 34 hours to erect?

Solution

We first get the z score for the two values. As z = (x - u) / s, then as          
x1 = lower bound =    32      
x2 = upper bound =    34      
u = mean =    32      
          
s = standard deviation =    2      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    0      
z2 = upper z score = (x2 - u) / s =    1      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.5      
P(z < z2) =    0.841344746      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.341344746 or 34.13% [ANSWER]