Bom dia!
O Intervalo de Confiança (IC) será dado por:
\(\displaystyle{IC=\overline{x}-Z_{\dfrac{\alpha}{2}}\cdot\dfrac{\sigma}{\sqrt{n}}<\mu<\overline{x}+Z_{\dfrac{\alpha}{2}}\cdot\dfrac{\sigma}{\sqrt{n}}}\)
Consultando-se uma tabela para obter \(Z_{\dfrac{\alpha}{2}}\), com \(\alpha/2=5\%/2=0,025\),
devemos procurar por \(P(Z>Z_{\dfrac{\alpha}{2}})=0,5-0,025=0,475\). Obtemos \(Z_{\dfrac{\alpha}{2}}=1,96\)
Então:
\(IC=1\,014-1,96\cdot\dfrac{25}{\sqrt{20}}<\mu<1\,014+1,96\cdot\dfrac{25}{\sqrt{20}}\\\\
IC=1\,014-1,96\cdot 5,59<\mu<1\,014+1,96\cdot 5,59\\\\
\fbox{IC=1\,003<\mu<1\,025}\)
Espero ter ajudado!