Entrainment processes in convective clouds often occur stochastically and entrainment rate estimates depend on the distance from the cloud from which the dry air is entrained. However, no observational studies exist on either the distance dependence or probability density function of entrainment rate, hindering understanding and the parameterization of convection. Here entrainment rate in cloud cores is estimated using a recently developed mixing fraction approach that is applied to in situ aircraft measurements of cumuli from the RACORO field program. The results are used to examine, for the first time, probability density functions of entrainment rate and their dependence on the distance from the edge of the cloud core from which the dry air is entrained. The estimated entrainment rate decreases when the dry air is entrained from increasing distance from the edge of the cloud core; this is because the air farther from the edge of the cloud core is drier than the neighboring air that is within the humid shell around the cumulus cloud core. Probability density functions of entrainment rate vary with the distance and height above the cloud-base, and all are well fitted by lognormal distributions. The implications of the results for convection parameterizations are discussed.