Distribusi normal

Diketahui \(\mu=72\) , \(n=150\), \(\sigma=9\)
Dapat diselesaikan menggunakan tabel Z
A. \[\begin{aligned}P(60<X<77)&=P(X<77)-P(X<60)\\&=P\left(Z<\frac{77-72}{9}\right)-P\left(Z<\frac{77-72}{9}\right)\\&=P(Z<0\text{,}56)-P(Z<-1\text{,}33)\\&=0\text{,}7123-0\text{,}0918\\&=0\text{,}6205\end{aligned}\]
Banyaknya memperoleh nilai 60 sampai 77
\[\begin{aligned}n_{60<x<77}&=n×P(60<X<77)\\&=150×0\text{,}6205\\&=93\text{,}75\\&=94\end{aligned}\]
B. \[\begin{aligned}P(X<70)&=P(Z<70)\\&=P\left(Z<\frac{70-72}{9}\right)\\&=P\left(Z<-0\text{,}22\right)\\&=0\text{,}4129\end{aligned}\]
C.\[\begin{aligned}P(X>65)&=1-P(Z<65)\\&=1-P\left(Z<\frac{65-72}{9}\right)\\&=1-P\left(Z<-0\text{,}78\right)\\&=1-0\text{,}2177\\&=0\text{,}7823\end{aligned}\]
D. misalkan x =10 % nilai tertinggi
\[\begin{aligned}Z_{1-\alpha/2}&=Z_{1-(0\text{,}1/2)}\\&=Z_{0,9500}\\&=1\text{,}64\end{aligned}\]
\(P(Z>z)\) =10% (dari tabel Z diperoleh z=1,64)
\[\begin{aligned}Z&=\frac{x-\mu}{\sigma }\\1\text{,}64&=\frac{x-72}{9}\\14\text{,}76&=x-72\\x&=84\text{,}76\end{aligned}\]