Final answer:
When all observations in a distribution are multiplied by a constant, the standard deviation also gets multiplied by that constant. In this case, the result to the standard deviation when all observations are multiplied by 2 is 12.
Step-by-step explanation:
To find the result to the standard deviation when all observations are multiplied by 2, we need to understand how standard deviation behaves when observations are multiplied by a constant. When all observations in a distribution are multiplied by a constant, the standard deviation also gets multiplied by that constant. In this case, since the standard deviation is 6, when all observations are multiplied by 2, the result would be 12.
The standard deviation of a distribution measures the amount of variation or dispersion in the set of values. When you multiply all observations in a data set by a constant, the standard deviation of the distribution is also multiplied by that constant (assuming the constant is positive, since standard deviation is always non-negative).
Given that the original standard deviation is 6 and all observations are multiplied by 2, we apply the rule above: New standard deviation = Original standard deviation * Multiplier Let's plug in the values: New standard deviation = 6 * 2 = 12 Therefore, the new standard deviation after all observations have been multiplied by 2 is 12. The correct answer is B. 12.