distribusi prob.normal

Question

SUATU MESIN MEMPRODUKSI KANCING YANG 20% CACAT. DIAMBIL SAMPEL ACAK SEBANYAK 500 KANCING YANG DIPRODUKSI MESIN TSB.
	TENTUKAN PROB KANCING YANG CACAT  :
	a. PALING BANYAK 150 BUAH
	b. ANTARA 135 – 165 BUAH
	c. 175 ATAU LEBIH

rahmayetty · Answer

Diketahui
$p=0,2$, $n=500$, maka $q=0,8$
$$\begin{aligned}\sigma &= n.p.q\&=500×0,2×0,8\&=80\end{aligned}$$
$$\begin{aligned}\mu&=n.p\&=500×0,2\&=100\end{aligned}$$
A. $$\begin{aligned}P(X<150)&=P(Z<150)\&=P\left(Z<\frac{150-100}{80}\right)\&=P\left(Z<0\text{,}63\right)\&=0\text{,}7357\end{aligned}$$
B. $$\begin{aligned}P(135<X<165)&=P(X<135)-P(X<165)\&=P\left(Z<\frac{165-100}{80}\right)-P\left(Z<\frac{135-100}{80}\right)\&=P(Z<0\text{,}81)-P(Z<0\text{,}44)\&=0\text{,}7910-0\text{,}6700\&=0\text{,}121\end{aligned}$$
C.  $$\begin{aligned}P(X>175)&=1-P(Z<175)\&=1-P\left(Z<\frac{175-100}{80}\right)\&=1-P\left(Z<0\text{,}94\right)\&=1-0\text{,}8264\&=0\text{,}1736\end{aligned}$$