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

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... . 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.