\(3\text{ hr }50\text{ min }=230\text{ min }\)
\(3\text{ hr }20\text{ min }=200\text{ min }\)
\(\mathbb P(X<200)=\mathbb P\left(\dfrac{X-230}{30}<\dfrac{200-230}{30}\right)=\mathbb P(Z<-1)\approx0.1587\)
(Same answer using the empirical rule: recalling that approximately 68% of a normal distribution lies within one standard deviation of the mean, so that 32% lies without, and due to symmetry of the distribution you know that approximately 16% of the distribution lies to the left of one standard deviation from the mean.)
