Final answer:
The question relates to normal distributions and involves finding probabilities for individual occurrences and sample means. It requires an understanding of z-scores and the Central Limit Theorem.
Step-by-step explanation:
The student's question revolves around the concept of a normal distribution in statistics. Specifically, the distance that fly balls travel in baseball, which are assumed to be normally distributed with a given mean and standard deviation. In parts of the question, the probability of a single fly ball traveling a certain distance is requested, as well as the probability related to the average distance of a group of fly balls.
For instance, if a single fly ball is randomly chosen from the distribution with mean 250 feet and standard deviation 50 feet, the probability of this ball traveling less than 220 feet would involve finding the z-score and then using the z-table or calculator to determine the corresponding probability. This is represented by P(X < 220) when X follows a normal distribution with a given mean and standard deviation.
The question regarding the average of 49 fly balls would require understanding the concept of the sampling distribution of the sample mean, which also follows a normal distribution with a new standard deviation equal to the population standard deviation divided by the square root of the sample size (the Central Limit Theorem).