Final answer:
The total weight of 11 randomly selected sumo wrestlers can be approximated as a normal distribution using the Central Limit Theorem, given the population mean and standard deviation of weights.
Step-by-step explanation:
The distribution of t = the total weight of 11 randomly selected sumo wrestlers can be approximated using the Central Limit Theorem if we know the mean weight and the standard deviation of the population of sumo wrestler weights. If the weights of sumo wrestlers are normally distributed, and we have the population mean (μ) and standard deviation (σ), then the sum of the weights (denoted as T for total weight) of 11 randomly selected sumo wrestlers would also be normally distributed with a mean μ_T= 11μ and a standard deviation σ_T= σ√11. In practice, sumo wrestler weights might not be perfectly normally distributed, but if the sample size is large enough, the Central Limit Theorem would still apply, giving a distribution that is approximately normal.
For instance, if it were known that sumo wrestlers have an average weight of 172 pounds with a standard deviation of 29 pounds (similar to the given example of men's weights), and you select 11 wrestlers at random, you could use these figures to calculate the probability of various total weights for the group of wrestlers.