The production of J/psi mesons in Z(0) decays is studied using 3.6 mil
lion hadronic events recorded by the OPAL detector at LEP. The inclusi
ve Z(0) to J/psi and b-quark to J/psi branching ratios are measured fr
om the total yield of J/psi mesons, identified from their decays into
lepton pairs. The J/psi momentum distribution is used to study the fra
gmentation of b-quarks. The production rate of psi' mesons, identified
from their decays into a J/psi and a pi(+)pi(-) pair, is measured as
well. The following results are obtained: Br(Z(0)-->J/psi X) = (3.9 +/
- 0.2 +/- 0.3). 10(-3) and Br(Z(0)-->psi' X) = (1.6 +/- 0.3 +/- 0.2).
10(-3), where the first error is statistical and the second systematic
. Finally the J/psi sample is used to reconstruct exclusive b-hadron d
ecays and calculate the corresponding b-hadron branching ratios and ma
sses.