Problem: Chocolate Chip Creators $($CCC$)$

CCC makes organic chocolate chips, sold mostly to firms that use them as ingredients for high$-$end, nutritious snack bars. Their process is very rigorous. The average diameter of their chocolate chips is $0\mathrm{.}5$ inches, with a standard deviation of $0\mathrm{.}05$ inches, and an upper and lower specification limit equal respectively to $0\mathrm{.}6$ and $0\mathrm{.}4$ inches.

$5.$

Question $5$

What is the capability index at CCC$?$

$1$ point

Enter answer here

$6.$

Question $6$

What is the probability that a chocolate chip falls outside the specification limits$?$

DO NOT WRITE AS A DECIMAL

$1$ point

Enter answer here

$7.$

Question $7$

What should their standard deviation be in order to achieve six sigma precision? $($Please format answer as a decimal: $0\mathrm{.}000)$