Source of randomness Is the random nature of all macroscopic phenomena like for example, turbulence or chemical kinetics ultimately traceable to quantum randomness?
 A: You are effectively asking "What is the relationship between quantum mechanics and classical chaos?" This is an open question and an intense area of study, known as quantum chaos. Stack exchange questions on quantum chaos have already been asked here (in a general context), here (in the context of predicting the weather), here (in the context of the double pendulum), and here (in the context of predicting the brain).
But in short, I'd answer your question like this:
If quantum mechanics was completely deterministic, chaotic macroscopic phenomena would still appear unpredictable to us, just because we will never know the initial conditions perfectly, and chaos exponentially amplifies uncertainty. But if you ask whether quantum mechanics makes most chaotic systems fundamentally unpredictable, then I'd say yes. Chaos can be one of many mechanisms by which quantum uncertainties / fluctuations have very macroscopic consequences.
However the precise understanding of classical chaos from a quantum mechanical perspective is difficult, because the Schrodinger equation is entirely linear, and so at first glance does not seem to be able to produce chaos. A subtler treatment involving many-body interactions is needed, and is being actively researched.
A: No.Quantum randomness comes from the collapse of the wavefunction while the classical statistical randomness  is just our lack of ability to contruct measuring devices which dont change the states of the particles.
