a$.$ The correlation matrix below represents the relationship in the investment returns among three

financial investment portfolios $($A$,$ B$,$ and C$).$

A B C

A $10\mathrm{.}800\mathrm{.}02$

B $0\mathrm{.}8010\mathrm{.}78$

C $0\mathrm{.}020\mathrm{.}781$

i$.$ Describe the relationship among the three investment portfolios. $[4$ MARKS$]$

ii$.$ Suppose an investor intends to diversify his$/$her investment for optimum stability. In which

two portfolios can he$/$she invest to achieve this objective? Why? $[3$ MARKS$]$

b$.$ Statistical Quality Control

i$.$ A machine drills hole in a pipe with a mean diameter of $0\mathrm{.}532$ cm and a standard deviation

of $0\mathrm{.}002$ cm$.$ Calculate the control limits for mean of samples $5$