An online exam is attempted by 50 candidates out of 20 are boys. The average marks obtained by boys is 12 with 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 50 candidates then $μ + σ^{2}$ is equal to

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

answer is D.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Number of boys = 20
Number of girls = 30
$σ_{B}^{2} = 2, {\bar{X}}_{B} = 12 σ_{G}^{2} = 2$
${\bar{X}}_{G} = \frac{50 \times 15 - 20 \times 12}{30}$
$= \frac{510}{30} = 17 = μ$
Variance of 50 candidates
$σ^{2} = \frac{20 σ_{B}^{2} + 30 σ_{G}^{2}}{50} + \frac{20.30}{{(20 + 30)}^{2}} {({\bar{X}}_{B} - {\bar{X}}_{G})}^{2} = \frac{20 \times 2 + 30 \times 2}{50} = \frac{600}{2500} \times 25 = 8 μ + σ^{2} = 17 + 8 = 25$