The population mean on a standard I. Q. test equals 100. The standard deviation

Question

The population mean on a standard I. Q. test equals 100. The standard deviation equals 15. A sample of 25 kids from a private school averaged 110 on this may now be concluded that. Kids from this private are exceptionally high on this I. Q. test. Kids from this private school are about average on this I. Q. test. Each individual student in this school is below average on I. Q. Kids from this private school scored extremely low on this l. Q. test. Aliens have landed! These aliens look just like humans (they have two eyes, two arms, two legs, etc.). The mean height off these aliens is 67 inches. The standard deviation is 24 inches. The aliens all look alike in height The aliens are different some are like giants, some are like midgets when compared to us The aliens have the same amount of variability as we do on height. None of the above, maybe.

Explanation / Answer

(24)
z = (110 - 100)/(15/sqrt(25)) = 3.33
P(z>3.33) = 0.0004

Kids from this private school are exceptionally high on this IQ test

(25)
As we see the standard deviation in the height of aliens is 24 inches which is very high.

This means the aliens are different - some are like giants, some are like midgets when compared to us.

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