The average math SAT score is 522 with a standard deviation of 112. A particular high school claims that its students have unusually high math SAT scores. A random sample of 45 students from this...

The average math SAT score is

with a standard deviation of

A particular high school claims that its students have unusually high math SAT scores. A random sample of

students from this school was​ selected, and the mean math SAT score was

Is the high school justified in its​ claim? Explain.

because the​ z-score

is

since it

within the range of a usual​ event, namely within

of the mean of the sample means.