Answer
$\beta = 0.9905 $
Work Step by Step
It is given that;
mean life of stationary muons $\Delta t$ = 16 $\mu s$
mean life time at speed $\Delta t_{o}$ = 2.2 $\mu s$
For an observer moving with relative speed v , the measured time interval is :$\Delta t=\frac{\Delta t_{o}}{\sqrt (1-\frac{v^2}{c^2})}$
Since the speed parameter $\beta = v/c $,
$\Delta t=\frac{\Delta t_{o}}{\sqrt (1-\beta^2)}$
$\beta = \sqrt(1-(\frac{\Delta t_{o}}{\Delta t})^2)$
$\beta = \sqrt(1-(\frac{2.2}{16})^2)$
$\beta = 0.9905$
