Marks obtained by students of a school in Economics subject follows normal distribution with mean $\mu$ and standard deviation $\sigma$. The value of standard score that a randomly selected student obtained 60 marks is 1. If the variance of variable is 100 (marks)$^2$ then find average marks.

Question

Accepted Answer

Given $Z = 1$ for $X = 60$ and $\sigma^2 = 100$, so $\sigma = 10$. Since $Z = \frac{X - \mu}{\sigma}$, we get $1 = \frac{60 - \mu}{10}$, therefore $\mu = 60 - 10 = 50$.