Step-by-step Solution:

If the standard deviation of (x), (y), and (z) is (p), then the standard deviation of (3x + 5), (3y + 5), (3z + 5) is: \[\] The standard deviation measures variability, and it is only affected by scaling (multiplication) but not by adding a constant. The general rule is: \[\] - Scaling a variable by a constant (a) scales the standard deviation by ( |a| ). \[\] Adding a constant to all data points does not affect the standard deviation. \[\] Here, the transformation is (3x + 5), (3y + 5), (3z + 5). The scaling factor is (3). \[\] Therefore, the new standard deviation becomes: |3| \(\times\) p = 3p \[\] \[\] \[\] Correct Answer: (b)