The average math SAT score is 521 with a standard deviation of 112. A particular high school claims that its students have unusually high math SAT scores. A random sample of 60 students from this school wasselected, and the mean math SAT score was 565. Is the high school justified in its claim? Explain.

(Yes, No), because the z-score ( enter your response here) is ▼ (not unusual, unusual) since it ▼ (lies, does not lie) within the range of a usual event, namely within ▼ (1 standard deviation, 2 standard deviations, 3 standard deviations) of the mean of the sample means. (Round to two decimal places as needed.)