已知 $\cos 2 \theta=\frac{\sqrt{2}}{3}$, 则 $\sin ^{4} \theta+\cos ^{4} \theta$ 的值为 $(\quad)$
[解析] $\sin ^{4} \theta+\cos ^{4} \theta=\left(\sin ^{2} \theta+\cos ^{2} \theta\right)^{2}-2 \sin ^{2} \theta \cos ^{2} \theta$

$=1-\frac{1}{2} \sin ^{2} 2 \theta=1-\frac{1}{2}\left(1-\cos ^{2} 2 \theta\right)=\frac{11}{18}$.