Answer to Question #336694 in Statistics and Probability for Koy

Question #336694

If a freshman is selected at random to become student assistant, what is the probability of selecting a student with an IQ between 90 and 120? Draw the normal curve.



1
Expert's answer
2022-05-04T12:09:58-0400

The office for admission of XYZ University found out that the IQ of incoming 1200 freshmen normally distributed with a mean of 108 and a standard deviation of 10.


P(90<X<120)=P(X<120)P(X90)P(90<X<120)=P(X<120)-P(X\le 90)

=P(Z<12010810)P(Z9010810)=P(Z<\dfrac{120-108}{10})-P(Z\le\dfrac{90-108}{10})

=P(Z<1.2)P(Z1.8)=P(Z<1.2)-P(Z\le-1.8)

0.884930.03593=0.8490\approx0.88493-0.03593=0.8490

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