Final answer:
Bob's distribution of lost golf balls is not uniform or symmetric, and given that there are more occurrences of lower numbers and fewer of higher numbers, the distribution is positively skewed.
Step-by-step explanation:
Given the list of lost golf balls Bob had during his eleven golf outings: 14, 7, 8, 7, 5, 8, 6, 7, 9, 12, 5, we can analyze the distribution of these numbers. To find out if the distribution is symmetric, positively skewed, negatively skewed, or uniform, we look for the characteristics such as the mean, median, mode, and the shape of the distribution when plotted as a histogram.
If the distribution was uniform, all the values would occur with the same frequency, and clearly that is not the case here since the values vary. A symmetric distribution would mean the data plots in a way where one half is the mirror image of the other. Since we have a high number like 14, which is not balanced by an equally low number, and the most frequent numbers (the mode) are around the middle (7), it is unlikely to be perfectly symmetric.
A positively skewed distribution is one in which the 'tail' of the distribution extends to the right, indicating more low-value numbers than high-value numbers. A negatively skewed distribution is the opposite, where the distribution’s tail extends to the left, indicating more high-value numbers.
In Bob's case, considering that there are more occurrences of lower numbers (e.g., 5 and 6) and less of higher numbers (particularly the single instance of 14), we can deduce that his distribution is positively skewed. This matches the principle that in a positively skewed distribution, the mode is often less than the median, which is less than the mean. Here, the mode is 7, which is more frequently occurring than other values, and the high values like 14 are less frequent. Therefore, the correct answer to the student's question is b) The distribution is positively skewed.