Question $4-$ Process Capability and Yield $(15\%)$

You are a manufacturer for a part used in automobiles. Based on your current process, you can make marts with the following statistics for part's length: mean $=1\mathrm{.}03cm$ and standard deviation $=0\mathrm{.}053cm.$ If your customers set the specs for the length as $0\mathrm{.}8cm-1\mathrm{.}2cm,$

What is your current production yield? $($note: yield is the probability that the products are within the specs$)(5\%)$

What would be your new yield if the customers tighten its specs to $0\mathrm{.}9cm-1\mathrm{.}1cm(5\%)$

If your customers are willing to pay $15\%$ more for the products with the new specs, should you make the change? $(5\%)$