A binomial distribution histogram presents as a sequence of bars whose heights reflect the probabilities of achieving a certain number of successes. Depending on the success probability, these histograms can appear symmetrical or skewed. It is a visual tool for understanding the distribution's shape, center, and variability.
A binomial distribution depicted on a histogram typically appears as a series of adjacent vertical bars. The heights of these bars represent the probability of observing a certain number of successes in a fixed number of trials. The x-axis usually represents the number of successes (from zero up to the number of trials), and the y-axis represents the probability of each number of successes occurring.
A histogram for a binomial distribution could look symmetrical or skewed, depending on the probability of success in each trial. For example, the graph of X~ B(20, .41) suggests relatively symmetrical distribution, given the success probability is close to 0.5. However, as the success probability moves away from 0.5, the histogram may become skewed. If the probability is very low or very high, the distribution will likely be skewed to the left or right, respectively.
Moreover, a histogram helps you visualize the nature of the distribution - its shape, center, and spread. The center, reflected in the mean, median, and mode, provides information about the most likely outcomes, while the spread indicates the variability of the data within the distribution.