Petrol Inc manufactures parts for an aircraft company It use

Petrol Inc. manufactures parts for an aircraft company. It uses a computerized numerical controlled (CNC) machining center to produce a specific part that has a design (nominal) target of 1.275 inches with tolerances of plusminus .024 inch. the CNC process that manufacturers these parts has a mean of 1.281 inches and a standard deviation of 0.008 inch. Determine the proportion of parts outside the specifications. Assume Normal Distribution.

Solution

Adding and subtracting the tolerance to the nominal target to get the upper and lower bound of the specification,

x1 = lower bound =    1.251      
x2 = upper bound =    1.299

We first get the z score for the two values. As z = (x - u) sqrt(n) / s, then as

x1 = lower bound =    1.251      
x2 = upper bound =    1.299      
u = mean =    1.281      
          
s = standard deviation =    0.008      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    -3.75      
z2 = upper z score = (x2 - u) / s =    2.25      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    8.84173E-05      
P(z < z2) =    0.987775527      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.98768711      

Thus, those outside this interval is the complement = 0.01231289   [ANSWER]