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The mean life of a sample of 60 bulbs was 650 h and the standard deviation was 8 h, If a second sample of 80 bulbs has a mean life of 660 h and standard deviation 7 h then find the over all standard deviation

Answer»


Solution :Here `n_(1)=60barx_(1)=650,s_(1)=8 ` and `n_(2)=80,barx_(2)=660,s_(2)=7`
`sigma=sqrt((n_(1)s_(1)^(2)+n_(2)s_(2)^(2))/(n_(1)+n_(2))+(n_(1)n_(2)(barx_(1) barx_(2))^(2))/(n_(1)+n_(2))^(2)`
`sqrt((60xx(8)^(2)+80xx(7)^(2))/(60+80)+(60xx80(650-660)^(2))/((60+80)^(2)))`
`sqrt((6xx64+8xx49)/(14)+(60xx80xx100)/(140xx140))`
`sqrt((192+196)/7+(1200)/49)=sqrt(388/7+1200/49)`
`sqrt((2716+1200)/49)=sqrt(3916/49)=62.58/7=8.9`


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