There rotten apples are mixed accidently with seven good apples and...

There rotten apples are mixed accidently with seven good apples,

And four apples are drawn one by one without replacement.

Now the random variable X denote the number of rotten apples.

And $\mu$ and ${\sigma}^{2}$ represent mean and variance of X, respectively,

So, now plotting the table of given data we get,

Now mean is given by, $∑ xP ( x ) = \dfrac{6}{2} = \mu$

And variance is given by ${\sigma}^{2} = ∑ {x}^{2}P ( x ) - {\mu}^{2}$

So, by putting the value from above table we get, ${\sigma}^{2} + {\mu}^{2} = 0 + \dfrac{1}{2} + \dfrac{12}{10} + \dfrac{9}{30} = 2$

Hence, $10\left({\sigma}^{2} + {\mu}^{2}\right) = 20$