Question

如果X 服从正态分布 N ( 2 ,25 ),计算概率P { | X |≤1 }.

Answer 1

P { | X |≤1 }=P { -1≤X ≤1 }

=P { (-1-2)/5≤(X-2)/5 ≤(1-2)/5 }=P { -3/5≤(X-2)/5 ≤-1/5 }=Ф(-0.2)-Ф(-0.6)

=1-Ф(0.2)-1+Ф(0.6)=Ф(0.6)-Ф(0.2)=0.7257-0.5739=0.1518