The observed fraction of Compton-thick AGN in the spectral bands 0.5−2, 0.5−8, 2−10 and 20−40 keV. Our model predictions for an intrinsic Compton-thick AGN fraction of 5, 15, 25% correspond to the the red dotted, blue short-dashed and green long dashed curves, respectively. The black solid lines are the predictions of the X-ray background synthesis model of Gilli et al. (2007). The magenta dot-dashed lines are the predictions of the Ballantyne et al. (2011) model. The inset plots show the predictions for the cumulative number counts of Compton-thick AGN. The curves are the same as in the main panels. The observational datapoints are from Tozzi et al. (2006) (2−10 keV), Brightman & Ueda (2012) (0.5−8 keV), Krivonos et al. (2007) adapted from Treister et al. (2009) (20−40 keV).