**Mean and Standard Deviation:**

The mean (a) and standard deviation (b) are two measures of central tendency and dispersion, respectively, used to describe a set of data.

- The mean (a) represents the average value of the data set.
- The standard deviation (b) measures the spread or dispersion of the data around the mean.

**SD of b a–x:**

To find the standard deviation of the expression b(a-x), we need to understand the properties of standard deviation.

- The standard deviation of a constant multiplied by a random variable is equal to the absolute value of the constant multiplied by the standard deviation of the random variable.
- The standard deviation of a constant added to a random variable remains the same as the standard deviation of the random variable.

**Calculating the Standard Deviation:**

Let's consider the random variable x with mean a and standard deviation b. We want to find the standard deviation of b(a-x).

1. First, let's calculate the mean of b(a-x):
- The mean of a random variable multiplied by a constant is equal to the constant multiplied by the mean of the random variable.
- Therefore, the mean of b(a-x) is b multiplied by the mean of (a-x), which simplifies to b(a-a).
- The mean of b(a-x) is 0.

2. Next, let's calculate the standard deviation of b(a-x):
- The standard deviation of a random variable multiplied by a constant is equal to the absolute value of the constant multiplied by the standard deviation of the random variable.
- The standard deviation of a constant added to a random variable remains the same as the standard deviation of the random variable.
- Therefore, the standard deviation of b(a-x) is equal to the absolute value of b multiplied by the standard deviation of (a-x).
- The standard deviation of (a-x) is the same as the standard deviation of x, which is b.
- Therefore, the standard deviation of b(a-x) is equal to the absolute value of b multiplied by b.
- This simplifies to b^2.

**Answer: (c) ab**

Therefore, the standard deviation of b(a-x) is equal to ab, which is option (c).

In conclusion, when the mean and standard deviation of x are a and b, respectively, the standard deviation of b(a-x) is ab.