Final answer:
The correct answer is option b, The correct answer to the student's question about the shape of a bimodal distribution is option b, indicating that a bimodal distribution has two obvious peaks.
Step-by-step explanation:
When describing a bimodal distribution, it is not necessary for the peaks to be of exactly equal height, nor do they need to be located in the middle of the distribution, and the term 'bimodal' inherently means two peaks, not two or more. A bimodal distribution can be visualized by a histogram with two distinct high points, representing the two modes, which are the most frequently occurring values in the data set. The mean, median, and mode could all differ in a bimodal distribution depending on the exact data points and the skewness of the distribution. It's also possible for a bimodal distribution to exhibit some skewness, where it might lean towards one side or the other, which can affect the mean and median's positioning in relation to the modes.
A bell-shaped distribution, in contrast, would have one peak and be perfectly symmetrical, meaning the mean, median, and mode all fall at the same central point. As for the Chebyshev's Rule, it applies to any type of distribution, whether it is bimodal or not, and describes the proportion of data that falls within a certain number of standard deviations from the mean.