(Solved): Consider a manufacturing process which includes FOUR sequential processes: P1, P2, P3 and P4. Every ...

1. Consider a manufacturing process which includes FOUR sequential processes: P1, P2, P3 and P4. Every manufactured product has to go through these processes sequentially. Each of the processes has a significant manual component and hence the time taken is a random variable. The respective times are as follows (all are in minutes): t1~N15, 2, t2~N35, 5, t3~N25, 4, and t4~N50, 6 
   
   
   (a) What is the average time taken to manufacture a single product? And what is the standard 
         deviation of the time?
   
   (b) What is the probability that a product will take between two hours, and two and a quarter
         hours to manufacture?
   
   (c) If your labor cost at the processes are as follows: Process1, $15/hour; Process2, $25/hour;

      Process3, $25/hour; and Process4, $40/hour, what are the mean and the standard
      deviation of cost of production for a unit of the product
 

    (d) If you are to supply an order of FIVE units, what is the average total time to
manufacture five units of the product and the standard deviation of producing the batch of
five units? (Hint: the time for each unit is a random variable)