The mean and standard deviation of 15 observations were found to be 12 and 3 respectively. On rechecking it was found that an observation was read as…

The mean and standard deviation of $\displaystyle 15$ observations were found to be $\displaystyle 12$ and $\displaystyle 3$ respectively. On rechecking it was found that an observation was read as $\displaystyle 10$ in place of 12. If $\displaystyle \mu$ and $\displaystyle \sigma^2$ denote the mean and variance of the correct observations respectively, then $\displaystyle 15\left(\mu+\mu^2+\sigma^2\right)$ is equal to $\displaystyle \_\_\_\_$.