  Strong mass loss on the red giant branch (RGB) can result in the formation of
extreme horizontal branch (EHB) stars. The EHB stars spend most of their He
core and shell burning phase at high temperatures and produce copious
ultraviolet flux. They have very small hydrogen envelopes and occupy a small
range in mass. We have computed evolutionary RGB models with mass loss for
stars with a range of metallicities at initial masses < 1.1 Msun corresponding
to populations ages between 12.5 and 14.5 Gyr. We used the Reimers formula to
characterize mass loss, but investigated a larger range of the mass loss
efficiency parameter, eta, than is common. To understand how the number of EHB
stars varies with metallicity in a stellar population we considered how the
zero-age horizontal branch (ZAHB) is populated. The range in eta producing EHB
stars is comparable to that producing `mid-HB' stars. Somewhat surprisingly,
neither the range nor magnitude of eta producing EHB stars varies much
metallicity. In contrast, the range of eta producing mid-HB stars decreases
with increasing metallicity. Hence the HB of populations with solar metallicity
and higher, such as expected in elliptical galaxies and spiral bulges, will be
bimodal if the distribution covers a sufficiently large range in eta.
