Supplier A makes a part for Company G.  The difference between the actual and desired length of a part is called D (measured in decimeters).  D is negative if A makes the part too short (desired is longer than actual).  Suppose D values are standard normal.

   a. What is the probability a part will miss the desired length by more than 0.44 decimeters (too long or too short)?

   b.    Let C be the cost of a part for G.  If the part is shorter than 0.44 decimeters, then the part must be returned for replacement.  The overall cost of such a part is $25.  If the part is too long by 0.44 decimeters or more, then the part can be shortened to meet standards.  The overall cost for such a part is $20.  If a part’s length is within 0.44 decimeters of the desired length, the quality of G’s product is unaffected.  The cost of such parts is $10.  Use your work in Part a and this information to represent the probability distribution of the random variable C.

        C                    P(C)            _

   c. Find E(C).   Interpret your result.