Notice how in problem 1 there is a sot of symmetry in that the energy from the energy to the band edge is the same for holes and electrons for the same doped carrier concentration. ("Carrier" is a general term that refers to either holes or electrons.)
However, in problem 4 that symmetry is gone. Because of the higher state density in the valence band, one achieves the same carrier concentration with a mu that is further from the relevant band edge.
In this "asymmetric" model, one also finds that in the undoped (intrinsic) circumstance, mu is not in the exact center of the gap (and the n_i and p_i are a little higher because the state density is higher.
(It is important to carefully distinguish between state density and carrier density in your thinking and your language. The later depends on mu, the former does not.)
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