IR-TST 2002 Problem 6

Assume $x_{1},x_{2},\dots,x_{n}\in\mathbb R^{+}$ , $\sum_{i=1}^{n}x_{i}^{2}=n$ , $\sum_{i=1}^{n}x_{i}\geq s>0$ and $0\leq\lambda\leq1$ . Prove that at least $\left\lceil\frac{s^{2}(1-\lambda)^{2}}n\right\rceil$ of these numbers are larger than $\frac{\lambda s}{n}$ .