Final answer:
To find the new standard deviation, each data value in the population is multiplied by 3 and the variance is multiplied by 9. The answer is D) 6√3.
Step-by-step explanation:
To find the new standard deviation, we need to understand the relationship between variance and standard deviation. The variance of a data set is the average of the squared differences from the mean, while the standard deviation is the square root of the variance.
In this case, each data value in the population is multiplied by 3, which means the variance is also multiplied by 3^2 = 9. So the new variance is 12 * 9 = 108.
Finally, to find the new standard deviation, we take the square root of the new variance. √108 = 6√3. Therefore, the answer is D) 6√3.