Distribusi normal

Diketahui \(\sigma=0\text{,}25\) dan \(\mu=4\text{,}54\)
Pertanyaan diatas dapat diselesaikan menggunakan Tabel Z
\[\begin{aligned}Z&=\frac{X-\mu}{\sigma }\end{aligned}\]

a. Lebih dari 5
\[\begin{aligned}P(X>5)&=1-P(Z<5)\\&=1-P\left(Z<\frac{5-4\text{,}54}{0\text{,}25}\right)\\&=1-P\left(Z<1\text{,}84\right)\\&=0\text{,}0329\end{aligned}\]

b. Kurang dari 4
\[\begin{aligned}P(X<4)&=P(Z<4)\\&=P\left(Z<\frac{4-4\text{,}54}{0\text{,}25}\right)\\&=P\left(Z<-2\text{,}16\right)\\&=0\text{,}0154\end{aligned}\]

c. Antara 4,4 sampai 4,6
\[\begin{aligned}P(4\text{,}4<X<4\text{,}6)&=P(Z<4\text{,}6)-P(Z<4\text{,}4)\\&=P\left(Z<\frac{4\text{,}6-4\text{,}54}{0\text{,}25})-P(Z<\frac{4\text{,}4-4\text{,}54}{0\text{,}25}\right)\\&=P\left(Z<0\text{,}24\right)-P\left(Z<-0\text{,}56\right)\\&=0\text{,}5984-0\text{,}2877\\&=0\text{,}3107\end{aligned}\]

d. Lebih dari 4,4
\[\begin{aligned}P(X>4\text{,}4)&=1-P(Z<4\text{,}4\\&=1-P\left(Z<\frac{4\text{,}4-4\text{,}54}{0\text{,}25}\right)\\&=1-P\left(Z<-0\text{,}56\right)\\&=0\text{,}7123\end{aligned}\]