Question

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

Answer 1

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)

$P(112<X<132)=P(\frac{112-100}{15}<Z<\frac{132-100}{15})=\\= P(0.8<Z<2.13)=P(Z<2.13)-P(Z<0.8)=\\=0.9834-0.7881=0.1953.$