The Boeing 7878 Dreamliner is designed to be 186 feet in len

The Boeing 787-8 Dreamliner is designed to be 186 feet in length. The manufacturing process for assembling the 787-8 follows a bell shaped symmetric distribution with mean 185.4 feet and standard deviation 0. 5 feet. What proportion of the 787-8 airplanes are between 185’ and 187’?

Determine the distribution along with the answer

Solution

This is a normal distribution.

We first get the z score for the two values. As z = (x - u) sqrt(n) / s, then as          
x1 = lower bound =    185      
x2 = upper bound =    187      
u = mean =    185.4      
          
s = standard deviation =    0.5      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    -0.8      
z2 = upper z score = (x2 - u) / s =    3.2      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.211855399      
P(z < z2) =    0.999312862      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.787457463   [ANSWER]