Sperry, Inc., an equipment manufacturer in Philadelphia, has submitted a sample water pressure control valve to improve flow capability in the manufacturing process. Your process engineering department has conducted experiments and found that the valve has a mean $()$ of $50\mathrm{.}22$ and a standard deviation $()$ of $\mathrm{.}05.$ Your desired performance is $=50+-3,$ where $=\mathrm{.}112.$

a$.$ What is the specification index of the Sperry valve

b$.$ Does this meet process specifications?