To determine the new standard deviation when each value in a data set is multiplied by a constant factor, we follow these steps:
1. Start with the original standard deviation of the data set. Here, the original standard deviation is 18.
2. When each data point in the set is multiplied by a constant factor, the standard deviation of the new data set is also multiplied by the same factor. In this case, the factor is 1.5.
3. To find the new standard deviation, multiply the original standard deviation by the given factor:
[tex]\[
\text{New standard deviation} = \text{Original standard deviation} \times \text{Factor} = 18 \times 1.5
\][/tex]
4. Carry out the multiplication:
[tex]\[
18 \times 1.5 = 27
\][/tex]
So, the standard deviation of the new data set will be 27.
Therefore, the correct answer is:
B. 27
