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 σ 2 is the variance of marks of 50 candidates, then μ + σ 2 is equal to

Step-by-step solution

20 Boys, 30 Girls σ B 2 = 2 , X ¯ B = 12 σ G 2 = 2 X ¯ G = 50 × 15 − 20 × 12 30 = 510 30 = 17 = μ Variance of 50 condidates σ 2 = 20 σ B 2 + 30 σ G 2 20 + 30 + 20 ⋅ 30 ( 20 + 30 ) 2 X ¯ B − X ¯ G 2 = 20 × 2 + 30 × 2 50 + 600 2500 ( 25 ) = 8 μ + σ 2 = 17 + 8 = 25