Question $11,$ Problem $17\mathrm{.}13$

HW Score: $88\%,88$ of $100$ points

Part $2$ of $2$

Points: $4$ of $8$

Rick Wing, salesperson for Wave Soldering Systems, Inc. $($WSSI$),$ has provided you with a proposal for improving the temperature control on your present machine. The machine uses a hot$-$air knife o cleanly remove excess solder from printed circuit boards; this is a great concept, but the hot$-$air temperature control lacks reliability. According to Wing, engineers at WSSI have improved the reliability of the critical temperature controls. The new system still has the four sensitive integrated circuits controlling the temperature, but the new machine has a backup for each. The four integrated circuits have reliabilities of $0\mathrm{.}82,0\mathrm{.}84,0\mathrm{.}86,$ and $0\mathrm{.}88.$ The four backup circuits all have a reliability of $0\mathrm{.}82.$

a$)$ The overall reliability of the new temperature controller $=89\mathrm{.}63\%($enter your response as a percentage rounded to two decimal places$).$