Quality characteristic of a product is normally distributed with a mean value of $10\mathrm{.}002mm$ and standard deviation of $0\mathrm{.}007mm.$ Design tolerances for this quality characteristic are $10+-0\mathrm{.}020mm.$

a$)$ Determine the probability that the tolerances will be violated.

$)$

$($ Violated

b$)$ Determine the number of products that will be out of tolerance if $10,000$ parts are manufactured.

Number of Bad Parts $=$

c$)$ What is one way to minimize the numberNew Number of Bad Parts$=$ of parts produced out of tolerances by setting up the machine and how much the number will be reduced?