Final answer:
The correct relationship is that the probability distribution would be skewed to the left if the mean of X is less than the median of X, as the mean is pulled toward the tail of the distribution.
Step-by-step explanation:
When comparing the mean and the median to determine the shape of a probability distribution, we rely on the general rule that if the distribution is skewed to the left, the mean is less than the median. Conversely, if the distribution is skewed to the right, the mean is greater than the median. This relationship is due to the way the mean takes into account all of the data values, and thus, it gets pulled in the direction of the tail of the distribution. For a symmetrical distribution, the mean and the median are roughly the same.
In the case where the mean of X is less than the median of X, the probability distribution would be skewed to the left. This is incorrect in the options provided as they suggest the distribution being skewed to the right or symmetric when the mean is less than the median. The correct relationship would be: The probability distribution is skewed to the left. This relationship makes sense because the mean of X is less than the median of X.