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The average math SAT score is 519 with a standard deviation of 111. A particular high...

The average math SAT score is 519 with a standard deviation of 111. A particular high school claims that its students have unusually high math SAT scores. A random sample of 45 students from this school was​ selected, and the mean math SAT score was 563. Is the high school justified in its​ claim? Explain.

____because the​ z-score ​( ​) ______since ______within the range of a usual​ event, namely within __________of the mean of the sample means.

​(Round to two decimal places as​ needed.)

Math   Statistics-And-Probability   
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Answer #1

= 519

= 111

n = 45

Sample mean, = = 519

Standard error, =

=

= 16.547

Z score corresponding to 563 is (563 - )/

= (563 - 519)/16.547

= 2.66

The high schools claim is justified because the z score is 2.66. Since it is not within the range of a usual event, namely within 2 standard deviation of distribution of sample mean (standard error) of the mean of sample means.

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