Based on the Normal model N(100,15) describing IQ scores, what percent of people's IQs would you expect to be: a) over 80% b) under 90% c) between 112 and 132
a)
"P(X>80)=P(Z>\\frac{80-100}{15})=P(Z>-1.33)=\\\\=1-P(Z<-1.33)=0.9082."
b)
"P(X<90)=P(Z<\\frac{90-100}{15})=P(Z<-0.67)=0.2514."
c)
"P(112<X<132)=P(\\frac{112-100}{15}<Z<\\frac{132-100}{15})=\\\\=\nP(0.8<Z<2.13)=P(Z<2.13)-P(Z<0.8)=\\\\=0.9834-0.7881=0.1953."
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