과제4

\begin{align*} &z \sim N(0, 1). \\[10pt] &~P(a < Z < b) \\[10pt] =~~&P\bigg( {a-0 \over 1} < {Z-0 \over 1} < {b-0 \over 1} \bigg) \\[15pt] &\text{표준정규분포는 좌우대칭.} \\[5pt] &\text{넓이가 가장 작으려면 a = -b 가 되어야 한다.} \\[15pt] =~~&P\bigg( -Z_{\alpha/2} < {Z-0 \over 1} < Z_{\alpha/2} \bigg) \\[15pt] =~~&P\bigg( -Z_{\alpha/2} < Z < Z_{\alpha/2} \bigg) \\[15pt] =~~& 1-\alpha \end{align*}

\begin{align*} \therefore ~~~&a =-Z_{\alpha/2} \\[5pt] ~&b =~Z_{\alpha/2} \end{align*}