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A(a,b)/6]^{\\lambda}[C^{1/6}(a,b)A^{5/6}(a,b)]^{1-\\lambda}<M(a,b) &\\qquad<[C(a,b)/6+5 A(a,b)/6]^{\\mu}[C^{1/6}(a,b)A^{5/6}(a,b)]^{1-\\mu} hold for all $a,b>0$ with $a\\neq b$, where $M(a,b)$, $A(a,b)$ and $C(a,b)$ denote the Neuman-S\\'andor, arithmetic, and contra-harmonic means of $a$ and $b$, 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