Answer
The sound intensity level would be $~29.0~dB$
Work Step by Step
We can find the intensity when the intensity level is 38.0 dB:
$10~log~\frac{I}{I_0} = \beta$
$10~log~\frac{I}{I_0} = 38.0$
$log~\frac{I}{I_0} = 3.80$
$\frac{I}{I_0} = 10^{3.80}$
$I = 10^{3.80}~I_0$
$I = 10^{3.80}~(1.0\times 10^{-12}~W/m^2)$
$I = 6.31\times 10^{-9}~W/m^2$
We can find the intensity of one violin:
$I' = \frac{I}{8} = \frac{6.31\times 10^{-9}~W/m^2}{8} = 7.89\times 10^{-10}~W/m^2$
We can find the sound intensity level of one violin:
$\beta = 10~log\frac{I'}{I_0}$
$\beta = 10~log\frac{7.89\times 10^{-10}~W/m^2}{1.0\times 10^{-12}~W/m^2}$
$\beta = 10~log~(789)$
$\beta = 29.0~dB$
The sound intensity level would be $~29.0~dB$.
