A company sells concrete in batches of 5 cubic yards. The probability distribution of \(X\), the number of cubic yards sold in a single order for concrete from this company, is shown in the table below.

$$ \begin{array}{|l|c|c|c|c|c|} \hline X = \text{ the number of cubic yards} & 10 & 15 & 20 & 25 & 30 \\ \hline \text{Probability} & 0.15 & 0.25 & 0.25 & 0.30 & 0.05 \\ \hline \end{array} $$

The expected value of the probability distribution of \(X\) is \(19.25\) and the standard deviation is \(5.76\). There is a fixed cost to deliver the concrete. The profit Y, in dollars, for a particular order can be described by \(Y= 75X-100 \). What is the standard deviation of \(Y\) ?

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The given value for the standard deviation of \(X\) is 5.76. When transforming data, a multiplication by a factor of 75 will result in a standard deviation multiplied by the same factor. Subtracting 100 from all values does not change the spread of the data.

$$ 5.76\cdot75=432 $$