  While Jupiter's massive gas envelope consists mainly of hydrogen and helium,
the key to understanding Jupiter's formation and evolution lies in the
distribution of the remaining (heavy) elements. Before the Juno mission, the
lack of high-precision gravity harmonics precluded the use of statistical
analyses in a robust determination of the heavy-elements distribution in
Jupiter's envelope. In this paper, we assemble the most comprehensive and
diverse collection of Jupiter interior models to date and use it to study the
distribution of heavy elements in the planet's envelope. We apply a Bayesian
statistical approach to our interior model calculations, reproducing the Juno
gravitational and atmospheric measurements and constraints from the deep zonal
flows. Our results show that the gravity constraints lead to a deep entropy of
Jupiter corresponding to a 1 bar temperature 5-15 K higher than traditionally
assumed. We also find that uncertainties in the equation of state are crucial
when determining the amount of heavy elements in Jupiter's interior. Our models
put an upper limit to the inner compact core of Jupiter of 7 Earth masses,
independently on the structure model (with or without dilute core) and the
equation of state considered. Furthermore, we robustly demonstrate that
Jupiter's envelope is inhomogenous, with a heavy-element enrichment in the
interior relative to the outer envelope. This implies that heavy element
enrichment continued through the gas accretion phase, with important
implications for the formation of giant planets in our solar system and beyond.
