Motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process. Assume a production process produces items with a mean weight...

Motorola used the
normal
distribution
to determine the probability of defects and the number of defects expected in a production process. Assume a production process produces items with a mean weight of 10 ounces.

1. The process standard deviation is 0.15 and the process control is set at plus or minus on standard deviation, so units with weights less than 9.85 oz or greater than 10.15 oz will be classified as defects. Find the probability of a defect
   and
   the expected number of defects for a 1000-unit production run.

1. Through process design improvements, suppose the process standard deviation can be reduced to 0.05. Assume the process control remains the same, so products with weights less than 9.85 and more than 10.15 ounces are classified as defects.  Find the probability of a defect
   and
   the expected number of defects for a 1000-unit production run.

1. What is the advantage of reducing process variation (question 2)? In other words, explain (mathematically) why reducing the standard deviation to 0.05 but keeping the process controls at 9.85 and 10.15 ounces led to better production outcomes.