Final answer:
Without context or class size regulations, the maximum number of students allowed in a continuing education class cannot be determined. Calculating the average class size for the statistics classes and the mean of X involves using the capacities and quantities of distinguished classes.
Step-by-step explanation:
The maximum number of students allowed in any continuing education class is not provided in the details available. It is not possible to determine the maximum number of students solely based on the options provided (47, 50, 55, 49) without additional context or guidelines related to class size regulations.
Similarly, for the university statistics classes, the average class size can be calculated by totaling the capacity of all classes and dividing by the number of classes. To calculate the mean of the random variable X, representing the class size a randomly selected student is in, weights the class sizes by the number of classes of each size and divides by the total number of classes. The standard deviation of X requires computing the square root of the weighted average of the squared differences from the mean.