Find the mean and standard deviation of the sum of their scores.

Two random variables \(x\) and \(y\) are independent when the value of \(x\) does not affect the value of \(y\). When the variables are not independent, they are dependent. A new random variable can be formed by finding the sum or difference of random variables. If a random variable \(x\) has mean \(\mu_{x}\) and a random variable \(y\) has mean \(\mu_{y}\), then the means of the sum and difference of the variables are given by \(\mu_{x+y}=\mu_{x}+\mu_{y}\) and \(\mu_{x-y}=\mu_{x}-\mu_{y}\). If random variables are independent, then the variance and standard deviation of the sum or difference of the random variables can be found. So, if a random variable \(x\) has variance \(\sigma_{x}^{2}\) and a random variable \(y\) has variance \(\sigma_{y}^{2}\), then the variances of the sum and difference of the variables are given by \(\sigma_{x+y}^{2}=\sigma_{x}^{2}+\sigma_{y}^{2}\) and \(\sigma_{x-y}^{2}=\sigma_{x}^{2}+\sigma_{y}^{2}\).