  We report 250GHz (1.2mm) observations of redshift 1.8 < z < 2.8 optically
luminous (M_B < -27.0), radio quiet quasars using the Max-Planck Millimeter
Bolometer (MAMBO) array at the IRAM 30-metre telescope. Nine quasars were
detected and for 26 quasars 3-sigma flux density limits in the range 1.8 to
4mJy were obtained. Adopting a typical dust temperature of 45K, the millimeter
emission implies far-infrared (FIR) luminosities of order 10^13 Lo and dust
masses of ~10^8 Mo. Applying a statistical survival analysis to our total
sample of 43 detected and 95 undetected quasars at z~2 and z>4, we find that
there is no apparent difference in the FIR luminosities, hence the star
formation rates, of QSO at z~2 and at 3.6< z <5. This differs from radio
galaxies, for which the FIR luminosity was found to increase with redshift
(Archibald et al. 2001). We furthermore find that there is no strong
correlation between the far-infrared and optical luminosities, confirming
previous results obtained on smaller samples.
