To find the variance of the numbers k, k+1, k+2, we can use the formula for variance which is the average of the squared differences from the mean.
First, we need to find the mean of the three numbers.
Mean = (k + k + 1 + k + 2) / 3 = (3k + 3) / 3 = k + 1
So, the mean is k + 1.
Next, we find the squared differences from the mean for each number:
For k, the difference from the mean is k - (k+1) = -1. The squared difference is (-1)^2 = 1.
For k+1, the difference from the mean is (k+1) - (k+1) = 0. The squared difference is 0^2 = 0.
For k+2, the difference from the mean is (k+2) - (k+1) = 1. The squared difference is 1^2 = 1.
Now we can find the variance:
Variance = [(1^2 + 0^2 + 1^2) / 3] = 2/3 = 0.67 (rounded to two decimal places)
Therefore, the answer is option (A) 2/3 or as a percentage approximately 66.7%.