A company has $2$ salespeople, $A$ and $B$.
Salesperson $A$ calls $8$ people each day. For each person he contacts he has a $70\%$ chance of making a sale.
Salesperson $B$, who operates independently of $A$, contacts $12$ people daily. For each person she contacts, she has a $60\%$ chance of making a sale.
Find the mean and standard deviation for $A$, for $B$ and for total daily sales $A+B$.
My thought was to use the formula mean $=$ number of trials $*$ probability of success so:
$$ mu(A) = 8 * 0.7 = 5.6$$ and :$$ mu(B) = 12 * 0.6 = 7.2$$ then finally :$$ mu(A+B) = mu(A) + mu(B)$$
Then, standard deviation $std = \sqrt{np(1-p)}$
combined standard deviation using rules for standard deviation and independence is:
$$std (A+B) = \sqrt{var ( A) + var(B)}$$
I know the mean and standard deviations rules will work for the problem, but just unsure if I can apply the mean and standard deviation of the individual calculations as I have outlined above.
Edit: The tags should formally be Rules for Variances and Standard Deviations of Linear Transformation and Rules for Means