Online　product　reviews　in　the　internet　of　things　platform　have　important　implications　for　consumers＇　buying　decisions.　Considering　the　large　volume　and　discrete　stochastic　characteristics　of　online　review　information,　an　online　product　purchasing　decision　method　based　on　normal　stochastic　multi-criteria　decision　and　vertical　distance　method　is　proposed.　Firstly,　we　present　and　prove　the　weighted　arithmetic　average　operator　under　normal　stochastic　information　environment.　Then,　the　idea　of　vertical　projection　distance　is　introduced,　according　to　the　binary　structure　of　expectation　and　variance　in　the　stochastic　attribute　information,　a　nonlinear　programming　model　for　calculating　the　product　attribute　weights　is　designed.　Based　on　this,　the　weighted　arithmetic　average　operator　is　used　to　aggregate　the　decision　information　from　the　attribute　dimension,　and　the　priority　order　of　the　candidate　products　is　obtained　according　to　the　order　relation　of　the　binary　structure　of　normal　stochastic　attributes.　Finally,　a　case　study　of　mobile　phone　purchase　decision-making　is　carried　out　to　verify　the　rationality　and　practicability　of　this　method.