#$2)$ A manufacturing process requires drilling a hole in a part. The average diameter of the

hole is $49\mathrm{.}15mm,$ with a standard deviation of $0\mathrm{.}51mm.$ If the holes are too small, below the

lower specification of $47\mathrm{.}80mm,$ they must be redrilled $($reworked$.)$ However, if the holes are

too big, above the upper specification of $49\mathrm{.}80mm,$ the parts are scrapped. Assuming a normal

distribution, $(15$ points$)$

a$)$ What percent of the parts are scrapped?

b$)$ What percent of the parts are reworked?

If the process average is changed to $48\mathrm{.}50mm($standard deviation is unchanged$),$ with the new

average,

c$)$ What percent of the parts are scraped?

d$)$ What percent of the parts are reworked?

e$)$ If rework is more economical, is the change in the process average a wise decision?

EXPLAIN your answer.

#$3)$ Given that the customer's stated target value for the dimension of a part is $8\mathrm{.}45mm,$ with

the upper and lower specifications of$,$ US $=13\mathrm{.}62mm$ and the $LS=1\mathrm{.}75mm,$ if the process

average $=8\mathrm{.}50mm$ and the standard deviation $=2\mathrm{.}35mm,$ calculate and clearly state the process

capability index. $(10$ points$)$