▁on ▁I Q ▁tests . ▁Near ly ▁ 9 % ▁of ▁the ▁area ▁under ▁the ▁curve ▁is ▁in ▁the ▁interval ▁from ▁ 1 2 0 ▁to ▁ 1 4 0 ; ▁corresponding ly , ▁about ▁ 9 % ▁of ▁the ▁population ▁scores ▁between ▁ 1 2 0 ▁and ▁ 1 4 0 ▁on ▁I Q ▁tests , ▁etc . ▁Similarly ▁many ▁other ▁things ▁are ▁distributed ▁according ▁to ▁the ▁" bell - sh aped ▁curve ", ▁including ▁measurement ▁errors ▁in ▁many ▁physical ▁measurements . ▁Why ▁the ▁u bi qu ity ▁of ▁the ▁" bell - sh aped ▁curve "? ▁There ▁is ▁a ▁theoretical ▁reason ▁for ▁this , ▁and ▁it ▁involves ▁Fourier ▁transform s ▁and ▁hence ▁trig on ometric ▁functions . ▁That ▁is ▁one ▁of ▁a ▁variety ▁of ▁applications ▁of ▁Fourier ▁transform s ▁to ▁statistics . ▁ ▁Tr ig on ometric ▁functions ▁are ▁also ▁applied ▁when ▁statist icians ▁study ▁season al ▁periodic ities , ▁which ▁are ▁often ▁represented ▁by ▁Fourier ▁series . ▁ ▁Number ▁theory ▁There ▁is ▁a ▁hint ▁of ▁a ▁connection ▁between ▁trig on ometry ▁and ▁number ▁theory . ▁Lo os ely ▁speaking , ▁one ▁could ▁say ▁that ▁number ▁theory ▁de als ▁with ▁qual itative ▁properties ▁rather ▁than ▁quant itative ▁properties ▁of ▁numbers . ▁ ▁Dis card ▁the ▁ones ▁that ▁are ▁not ▁in ▁lowest ▁terms ; ▁keep ▁only ▁those ▁that ▁are ▁in ▁lowest ▁terms : ▁ ▁Then ▁bring ▁in ▁trig on ometry : ▁ ▁The ▁value ▁of ▁the ▁sum ▁is ▁− 1 , ▁because ▁ 4 2 ▁has ▁an ▁odd ▁number ▁of ▁prime ▁factors