Distribution of Δα_ox in the z ≃ 3 sample (see Sect. 2.3 for details). The dashed curve is the best fitting normal distribution for the 25 radio-quiet sources with unquestionable X-ray detection (we also neglected the radio-bright quasar J0900+42), where the peak position is forced to be at Δα_ox = 0. We define as X-ray-weak (W) and X-ray-weak candidates (w) all the sources at more than 3σ (seven objects, brown histogram) and 2σ (four objects, orange histogram) from the peak, respectively. All the other quasars are considered as X-ray normal (N, blue histogram).