An order for bottles of vitamins from a certain mail order company costs $\$ 12.04$ per bottle plus a shipping cost of $\$ 4.80$ regardless of the number of bottles ordered. Over the past year, the company has received 100 orders for bottles of vitamins, The standard deviation of the numbers of bottles per order for the 100 orders is 1.5 bottles. What is the standard deviation of the 100 costs for the orders?
The mean number of bottles per order is unknown.
The total number of bottles sold is unknown.
The total number of bottles equals $100 \ \cdot$ mean number of bottles per order.
$$\sqrt{ \dfrac{\sum_{i=1}^{100} (bottles_{ith \ order}-\dfrac{\sum bottles}{orders})^2}{100}}= standard \ deviation =\sqrt{\dfrac{ \sum_{i=1}^{100}(bottles_{ith \ order}-\dfrac{\sum bottles}{100})^2}{100}}=1.5$$.
$12.04 \sum bottles+4.8 \cdot orders=12.04 \sum bottles+4.8 \cdot 100 = total \ cost$
$\sum bottles = \dfrac{total \ cost - 4.8 \cdot 100}{12.04}$
How to proceed?
There is not enough info on the total number of bottles and its mean, so you should leave that out of the equation. Here is an idea: let $X$ denote your variable that is number of bottles per order, where $X \sim F(\mu, \sigma^2=1.5^2)$ distributed for unknown distribution function $F$. Let $Y$ denote the total cost of an order, where $Y \sim 4.80 + 12.04 \cdot X(\mu, 1.5^2) = 4.80 + \mu + 12.04 \cdot 1.5 \cdot X(0,1)$. Then we see that Y has mean $4.80 + \mu$ and standard deviation $12.04 \cdot 1.5$. This makes sense because the shipping cost (the same for every order) does not change the standard deviation of the order, only the bottles do.