1. **Stating the problem:** We want to find the mean and standard deviation of the total money collected from selling adult tickets at 10 each and children tickets at 6 each on a random Saturday, assuming the number of adult and children tickets sold are independent random variables. 2. **Formulas and rules:** - If $X$ and $Y$ are independent random variables, then the mean of their sum is $E(X+Y) = E(X) + E(Y)$. - The variance of their sum is $Var(X+Y) = Var(X) + Var(Y)$ because of independence. - The standard deviation is the square root of the variance: $\sigma = \sqrt{Var}$. 3. **Define variables:** Let $A$ be the number of adult tickets sold, and $C$ be the number of children tickets sold. The total money collected is $M = 10A + 6C$. 4. **Calculate mean of $M$:** $$E(M) = E(10A + 6C) = 10E(A) + 6E(C)$$ 5. **Calculate variance of $M$:** $$Var(M) = Var(10A + 6C) = 10^2 Var(A) + 6^2 Var(C) = 100 Var(A) + 36 Var(C)$$ 6. **Calculate standard deviation of $M$:** $$\sigma_M = \sqrt{Var(M)} = \sqrt{100 Var(A) + 36 Var(C)}$$ 7. **Summary:** - Mean money collected: $E(M) = 10E(A) + 6E(C)$ - Standard deviation: $\sigma_M = \sqrt{100 Var(A) + 36 Var(C)}$ To find numerical values, you need the means and variances of $A$ and $C$ (number of tickets sold).