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Question

An online exam is attempted by 50 candidates out of which 20 are boys. The average marks obtained by boys is 12 with a variance 2. The variance of marks obtained by 30 girls is also 2. The average marks of all 50 candidates is 15. If μ is the average marks of girls and σ2 is the variance of marks of 50 candidates, then μ+σ2 is equal to

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Solution

Sum of marks of boys, XB=240
Total marks X=750
So, sum of marks of girls =510=XG

X2B20(12)2=2 and X2G30(¯¯¯¯¯XG)2=2
X2B=2920 and X2G30(17)2=2
X2G=8730

Overall Variance=X2B+X2G50(¯¯¯¯¯X)2
=2920+873050(15)2=8
μ=17, σ2=8
μ+σ2=25

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