Diketahui
\[\begin{aligned}\mu&=500×0\text{,}5\\&=250\end{aligned}\]
\[\begin{aligned}\sigma&=\sqrt{500×0\text{,}5×0\text{,}5}\\&=11\text{,}18\end{aligned}\]
A. Probabilitas saat X bernilai \(250\pm10\)
Cari nilai \(X_{1}=250-10=240\)
\(X_{2}=250+10=260\)
Maka
\[\begin{aligned}P(X=240)&= P(Z= \frac{240-250}{11\text{,}8}\\&=P(Z=-0\text{,}89)\\&=0\text{,}3133\end{aligned}\]
\[\begin{aligned}P(X=260)&= P(Z= \frac{260-250}{11\text{,}8}\\&=P(Z=0\text{,}89)\\&=0\text{,}3133\end{aligned}\]
Jadi totalnya adalah \(0,3133+0,3133 = 0,6266\)
Atau sekitar 62,66%
B.Probabilitas saat X bernilai \(250\pm 30\)
Cari nilai \(X_{1}=250-30=220\)
\(X_{2}=250+30=280\)
Maka
\[\begin{aligned}P(X=220)&= P(Z= \frac{220-250}{11\text{,}8}\\&=P(Z=-2\text{,}68)\\&=0\text{,}4963\end{aligned}\]
\[\begin{aligned}P(X=280)&= P(Z= \frac{280-250}{11\text{,}8}\\&=P(Z=2\text{,}68)\\&=0\text{,}4963\end{aligned}\]
Jadi totalnya adalah \(0,4963+0,4963 = 0,9926\)
Atau sekitar 99,26%
