In general, can we say that micro-world is non-deterministic and macro-world is deterministic?
We know where a thrown stone will land, so why do some people say that the macro world is non-deterministic? Just because we can't measure something 100% accurately, that doesn't mean that the object is not there where nature's rules determine it to be.
Technically classical mechanics classical mechanics is a 100% deterministic theory. But when looking at more complicated systems it will get very chaotic very fast, which means your deterministic trajectory will depend very strongly on the initial conditions. That means if you want to make a prediction with sufficient accuracy for the trajectory in the arbitrarily far future you need exact initial conditions. But here the quantum uncertenties tell you that you can’t know your initial conditions arbitrarily exact. So chaos theory effectively transfers your quantum indeterminism into the macroscopic world if looking at time wise sufficiently long trajectories. Because the small difference causes by quantum uncertenties will be transferred into macroscopic differences eventually, if your system is sufficiently chaotic.
So in conclusions that means, that if the "micro-world" is non-deterministic the "macro-world" is also non-deterministic.
Roughly, if you consider the early matter wave approach by de Broglie, the wavelength $\lambda$ is inversely proportional to the momentum $p$ which in turn is proportional to the mass: $$\lambda = \frac{h}{p}=\frac{h}{mv}\sim \frac{1}{m}$$ Massive objects thus have a small de Broglie wavelength. The probability distribution is then much more sharply peaked. For macroscopic objects the peak is so sharp that the position of an object is known with a very high precision.
The world is not perfectly deterministic. But it isn't totally random either. Sometimes you can use the present to predict the future very well. Sometimes not so well.
One source of non-determinism is quantum uncertainty. We are used to thinking of a particle as a point with a perfectly defined position and momentum that we cannot measure perfectly. This leads to a perfectly defined trajectory.
The reality is that there is a range of positions where the particle might be. It does not have a position. Likewise there is a range of momenta the particle might have. Furthermore, if one range is small, the other must necessarily be big. This is expressed by the Uncertainty Principle, $\Delta x \Delta p > \hbar$.
These uncertainties lead to a range of trajectories the particle might have. You cannot predict exactly what trajectory the particle will take. But you do have some information. You can predict probabilities.
The limits on precision of position and momentum are the same size for all objects, big and small. But the effect is more noticeable for small objects.
You might want to find the trajectory of an electron orbiting a nucleus. The nucleus attracts the electron and tries to keep it very close. A small range of positions means a large range of momenta. An electron that might have a large momentum isn't likely to stay very close to a nucleus for long. This tends to keep the electron farther away. The size of an atom is determined by these competing tendencies. The range of positions an electron might have is the size of the atom. The electron doesn't have an orbit. It just has a range of positions and momenta near the nucleus. If you measure the position, it might be any one of them and it might be going in any direction. This is described as an electron cloud.
A stone has uncertainties the same size. If you determine the position of the stone with a precision of an atomic diameter, the stone will necessarily have a range of momenta as big as the electron does. This means if you throw the stone, the uncertainty of momentum would affect the trajectory as much as if an electron bumped it off course.
Quantum uncertainty limits the precision of macroscopic trajectories, but the effect is so small that we cannot detect it. It was not discovered until people studied subatomic particles.
