2. Information you need to know for this question: In the general population, IQ

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2. Information you need to know for this question: In the general population, IQ scores are distributed approximately normal with 100 and -15. A researcher develops a pill that she thinks will dramatically increase IQ scores. She finds a random individual and gives him this pill. After that, she measures his IQ, which turns out to be 140. The researcher is glad, because 140 is a really high IQ score (if a person's IQ is 130 or more he or she is considered a ‘genius') so it seems that maybe the pill worked. However, she also realizes that there may be another reason that her subject has a high IQ: Maybe she just picked an individual for her experiment that happens to have the extreme IQ score of 140 and the pill had nothing to with it. So there are two alternative explanations of why her sample individual has a high IQ: 1. His IQ is high due to the pill. 2. She just happened to have selected a person that had a very high IQ to begin with, and the pill had nothing to do with it. To decide between the two explanations she asks herself the following questions (please answer them for her) a. What percentage of the general population has an IQ score of 140 or more?

Explanation / Answer

SolutionA:

P(X>140)

z=x-mean/sd

=140-100/15

=40/15

=2.666667

P(Z>2.667)

=1-P(Z<2.667)

=1-0.9962

=0.0038

=0.0038*100

=0.38%

SOlutionb:

circle 263

SOlutionc:

P(X>140)

P(Z>2.667)

=1-P(Z<2.667)

=1-0.9962

=0.0038

ANSWER:0.0038

Solutiond:

P(X>-=140)

=P(Z>140-100/15/sqrt(1)

=P(Z>2.667)

=0.0038

Solutione:

probability of happening is very less

YES

Solutionf

she cannot reject explanation 2

she can reject explanation 1

NO

Solutiong:

it leaves her with explanation 2

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