Final answer:
The mean of the distribution is calculated using the given coefficient of variation (60%) and standard deviation (12). By applying the formula for the coefficient of variation, we solve for the mean and find it to be 20. Therefore, the mean of the distribution is 20. So the correct option is C. 20.
Step-by-step explanation:
The coefficient of variation (CV) is defined as the ratio of the standard deviation (\(\sigma\)) to the mean (\(\mu\)), expressed as a percentage. Given that the coefficient of variation is 60% and the standard deviation is 12, we can use the formula CV = \(\frac{\sigma}{\mu}\) \(\times\) 100% to find the mean. To find the mean of a distribution given the coefficient of variation and standard deviation, we can use the formula:
Mean = Standard Deviation / Coefficient of Variation
Plugging in the values, we get:
Mean = 12 / 0.6 = 20
Let's solve the equation step-by-step:
Convert the coefficient of variation into decimal form: 60% = 0.60.
Use the formula with the given standard deviation (\(\sigma\) = 12) to calculate the mean (\(\mu\)): CV = \(\frac{\sigma}{\mu}\) \(\times\) 100% or 0.60 = \(\frac{12}{\mu}\).
Now, solve for \(\mu\): \(\mu\) = \(\frac{12}{0.60}\) = 20.
Therefore, the mean of the distribution is 20. So the correct option is C. 20.