What are the two key considerations for the FED when it sets the Federal Funds rate $($from the article in FT$)?(2$ lines$)$

Why is the Federal Funds Rate important for fixed$-$income market participants $-$ why does it impact treasury prices of all maturities? $(3$ lines$)$

A Fed Fund futures contract is quoted at $$95.$ What is the implied average Federal Funds rate according to this contract?

If the Fed Fund futures price $($EFFR$)$ is $95$ at the start of month T $($end of last month T$-1)$ and is $95\mathrm{.}1$ for the end of month T$,$ what is the associated probability of a rate cut? Assume that the FOMC meeting is after $15$ days and the number of days in the month are $30?$