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The authors consider the mean-field version of a spin-1 Ising ferromagnet in a random crystal field described by a Gaussian probability distribution. Depending on the width of the Gaussian, they obtain a rich phase diagram, with critical and coexistence lines and some multicritical points. At low temperatures, their numerical results are supported by some analytic asymptotic expansions. They also calculate the ground state for a suitable two-valued delta-function distribution to compare with the results for the Gaussian case.