  (abridged): Low resolution spectroscopy obtained with FORS2 at the Very Large
Telescope (VLT) has been used to measure individual metal abundances ([Fe/H])
for 107 RR Lyrae stars, and trace the metal distribution of the oldest stellar
component in the Sculptor dwarf spheroidal galaxy. Their metallicities have an
average value of [Fe/H]=-1.83 +/- 0.03 (r.m.s. 0.26 dex) and cover the
metallicity range -2.40<[Fe/H]<-0.85 (only 1 star with [Fe/H]>-1). The
star-to-star scatter is larger than typical errors on individual metallicities
(+/- 0.15-0.16 dex), indicating a real spread in metal abundances. The radial
velocities have a dispersion of 12.9 km/s, consistent with the dispersion
derived in Sculptor by Tolstoy et al. (2004). This along with the metallicity
distribution, suggests that most of the RR Lyr's arise from the same burst of
stellar formation that produced the metal-poor component giving origin to the
galaxy blue horizontal branch, and only a few (if any) come from the centrally
concentrated metal-rich red horizontal branch population. The spectroscopic
metallicities and the apparent luminosities were used to study the
luminosity-metallicity relation, for which we derive a shallow slope of 0.09
mag/dex. This result can be due to a high level of evolution off the zero age
horizontal branch of the RR Lyrae stars in this galaxy, again in agreement with
their origin from the blue horizontal branch population.
