Six Sigma assumes that $1\mathrm{.}5$ standard deviations is normal variation. So $6$ Sigma is calculated using $4\mathrm{.}5$ standard deviations in the normal distribution $(6-1\mathrm{.}5=4\mathrm{.}5).$ It also uses the upper tail of the distribution. Knowing this information allows us to manually calculate defects per million opportunities $($DPMO$),$ an important statistic that indicates how a business process is performing! In Excel, $=$normsdist$()$ looks up values in the normal probability distribution, a distribution we will discuss later in the course but one with which you should have some familiarity. $=$normsdist$(4\mathrm{.}5)$ results in $0\mathrm{.}999996602326875,$ meaning that most of the entire area of the curve is within $6$ sigma. From this, we calculate that $3\mathrm{.}39767$E$-06$ of the area is outside of $6$ sigma to the right by subtracting $1-0\mathrm{.}999996602326875.$ If we multiply this number by $1,000,000,$ we get defects per million opportunities $($DPMO$)$ of about $3\mathrm{.}4.$ We now can calculate the DPMO for any value of Sigma.

Part $1.$ Divide your age by $100$ and add to $4.$ For example, my age is $56/100=\mathrm{.}56+4=4\mathrm{.}56.$ Assume that this is the sigma associated with a supply chain process $($e$.$g$.,$ delivery of undamaged goods to the customer$).$ Then calculate the DPMO associated with this value. Post your Excel formula. Example

$=(1-$NORMSDIST$(4\mathrm{.}56-1\mathrm{.}5))*1000000$

$1106\mathrm{.}685$ or about $1107$ defects per million opportunities.