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Given a permutation $\\sigma$ of $[n],$ let $\\mathbf{N}_{n}(\\sigma)$ denote the number of ways to write $\\sigma$ as a product of two involutions of $[n].$ If we endow the symmetric groups $S_{n}$ with uniform probability measures, then the random variables ${\\mathbf N}_{n}$ are asymptotically lognormal.\n  The proof is based upon the observation that, for most permutations $\\sigma$, $\\mathbf{N}_{n}(\\sigma)$ can be well approximated by $\\mathbf{B}_{n}(\\sigma),$ the product of the cycle lengths of $\\sigma$. 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Given a permutation $\\sigma$ of $[n],$ let $\\mathbf{N}_{n}(\\sigma)$ denote the number of ways to write $\\sigma$ as a product of two involutions of $[n].$ If we endow the symmetric groups $S_{n}$ with uniform probability measures, then the random variables ${\\mathbf N}_{n}$ are asymptotically lognormal.\n  The proof is based upon the observation that, for most permutations $\\sigma$, $\\mathbf{N}_{n}(\\sigma)$ can be well approximated by $\\mathbf{B}_{n}(\\sigma),$ the product of the cycle lengths of $\\sigma$. 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