An online exam is attempted by 50 candidates out of which 20 are boys.

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  is the average marks of girls and $\sigma^2$ is the variance of marks of 50 candidates, then $\mu+\sigma^2$ is equal to

Answer: 25

Accepted Answer

$$\bar X_G = \frac{50(15)-20(12)}{30} = \frac{510}{30}=17=\mu$$

$$\sigma^2 = \frac{20(2)+30(2)}{50}+\frac{20\times30}{50^2}(12-17)^2 = 2+\frac{600}{2500}\times25 = 2+6=8$$

$$\mu+\sigma^2 = 17+8=25$$

Solutions · 1