We are given the results of an inspection of fifty boxes of bolts, where the number of defective bolts per box and the number of boxes with that number of defective bolts are recorded. We are asked to find the mean and median of the distribution.

The mean is calculated by summing up all the values and dividing by the number of values. In this case, we can calculate the mean as follows:

Mean = (4 * 2 + 5 * 7 + 6 * 17 + 7 * 10 + 8 * 8 + 9 * 6) / 50

Mean = (8 + 35 + 102 + 70 + 64 + 54) / 50

Mean = (333) / 50

Mean ≈ 6.7

The median is the middle value when the data is arranged in ascending order. Since there are an even number of boxes, the median is the average of the two middle values. In this case, we can find the median by counting the number of boxes until we reach the middle two values:

- The first two boxes have 4 defective bolts.

- The next seven boxes have 5 defective bolts.

- The next seventeen boxes have 6 defective bolts.

Since we have reached the middle two values, which are both equal to 6, the median is equal to (6 + 6) / 2 = **6**.

So, the mean and median of the distribution are approximately **6.66 and 6**, respectively. This corresponds to answer choice **A**.