We address the very large diversity of the jet production efficiency in active galactic nuclei (AGNs) by using data on low redshift AGNs selected from the Swift/BAT catalog and having black hole (BH) masses larger than $10^{8.5},M_{odot}$. Most of these AGNs accrete at intermediate rates and have bolometric luminosities dominated by mid-IR radiation. Our sample contains $14%$ radio-loud (RL), $6%$ radio-intermediate (RI), and $80%$ radio-quiet (RQ) AGNs. All RL objects are found to have extended radio structures and most of them have classical FR II morphology. Converting their radio loudness to the jet production efficiency, we find that the median of this efficiency is on the order of $(epsilon_d/0.1)%$, where $epsilon_d=L_{rm bol}/dot{M}c^2$ is the radiation efficiency of the accretion disk. Without knowing the contribution of jets to the radio emission in the RQ AGNs, we are only able to estimate their efficiencies using upper limits. Their median is found to be $0.002(epsilon_d/0.1)%$. Our results suggest that some threshold conditions must be satisfied to allow production of strong, relativistic jets in RL AGNs. We discuss several possible scenarios and argue that the production of collimated, relativistic jets must involve the Blandford-Znajek mechanism and can be activated only in those AGNs whose lifetime is longer than the time required to enter the magnetically arrested disk (MAD). Presuming that MAD is required to collimate relativistic jets, we expect that the weak nonrelativistic jets observed in some RQ AGNs are produced by accretion disks rather than by rotating BHs.