We studied the relationship between the projected speed of coronal mass ejections (CMEs), determined from a sequence of Solar and Heliospheric Observatory/Large Angle and Spectrometric Coronagraph Experiment (SOHO/LASCO) images, and the hourly averaged magnitude of the Bz component of the magnetic field in an interplanetary ejecta, as measured by the Advanced Composition Explorer (ACE) magnetometer in the Geocentric Solar Magnetospheric Coordinate System (GSM). For CMEs that originate at the central part of the solar disk we found that the intensity of Bz is correlated with the projected speed of the CME, Vp. The relationship is more pronounced for very fast ejecta (Vp > 1200 km/s), while slower events display larger scatter. We also present data which support earlier conclusions about the correlation of Bz and the Dst index of geomagnetic activity. A possible application of the results to space weather forecasting is discussed.