An online exam is attempted by 40 candidates out of which 15 are boys. The average marks obtained by boys is 10 with variance 2. The variance of marks obtained by 25 girls is also 2 and the average marks of all 40 candidates is 12.5. If is average marks

Question

An online exam is attempted by 40 candidates out of which 15 are boys. The average marks obtained by boys is 10 with variance 2. The variance of marks obtained by 25 girls is also 2 and the average marks of all 40 candidates is 12.5. If $μ$ is average marks of the 25 girls & $σ^{2}$ is variance of marks of all 40 candidates then $20 σ^{2} - 8 μ$ = ______

Smart Achievers · Accepted Answer

(3)

$μ = \frac{40 \times 12.5 - 10 \times 15}{25} = 14$

$σ^{2} = 2 + \frac{15 \times 25}{40 \times 40} {(4)}^{2} = 5.75$

Solution

Ans.
(3)

$μ = \frac{40 \times 12.5 - 10 \times 15}{25} = 14$

$σ^{2} = 2 + \frac{15 \times 25}{40 \times 40} {(4)}^{2} = 5.75$

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Solution

Ans. (3) μ=40×12.5-10×1525=14 σ2=2+15×2540×40(4)2=5.75

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Ans.
(3)

$μ = \frac{40 \times 12.5 - 10 \times 15}{25} = 14$

$σ^{2} = 2 + \frac{15 \times 25}{40 \times 40} {(4)}^{2} = 5.75$