The average math SAT score is 520 with a standard deviation of 114. A particular high school claims that its students have unusually high math SAT scores. A random sample of 40 students from this school was selected, and the mean math SAT score was 553. Is the high school justified in its claim? Explain. Yes, because the z-score (2.61) is unusual since it does not lie within the range of a usual event, namely within 2 standard deviations of the mean of the sample means. (Round to two decimal places as needed.)