$1.$ In testing certain systems whose operating time up to failure was normally distributed, we obtain ten realizations of the operating time up to failure $($in hours$)$: $115,75,80,150,75,100,120,95,70,100.$

Find the confidence bounds for the mean of the operating time up to failure with a level of confidence of $.$

a$.70$ hr

b$.79\mathrm{.}10$ hr

c$.97$ hr

d$.75$ hr

$2.$ if a system has MTBF of $100$ hours and MTTR of $120$ minutes, then the availability is

Select one:

a$.0\mathrm{.}9975$

b$.0\mathrm{.}4545$

C$.0\mathrm{.}9804$

d$.0\mathrm{.}8333$

$3.$ A computer has an MTTF $$and an MTTR $.$

If the MTTR is reduced to $1\mathrm{.}5$ hr$,$ what MTTF can be tolerated without decreasing the availability of the computer?

a$.$

b$.22$

C$.20\mathrm{.}4$

d$.21\mathrm{.}35$

$4.$ Four capacitances of $$each are connected in parallel to act as a single capacitance of $$required for the successful operation of a unit. If the reliabilities of these capacitors are $,$ and $0\mathrm{.}9$ respectively, find the reliability of the unit.

a$.0\mathrm{.}31$

b$.0\mathrm{.}24$

C$.0\mathrm{.}3024$

d$.0\mathrm{.}29$

$5.$ A computer has an MTTF $$and an MTTR $.$ What is the availability?

a$.0\mathrm{.}9312$

b$.0\mathrm{.}8932$

C$.0\mathrm{.}9512$

d$.0\mathrm{.}9670$