4. If Xiaozhang's sleep time each day is randomly and uniformly distributed between 6 to 9 hours, then the probability that Xiaozhang's average sleep time over two consecutive days is no less than 7 hours is $\qquad$ .
4. $\frac{7}{9}$.

Let the hours of sleep that Xiao Zhang gets on two consecutive days be $x$ and $y$ $(x, y \in [6,9])$.

The possible events are denoted as $(x, y)$, corresponding to the points on the sides and within the square $ABCD$ in the coordinate plane.

Xiao Zhang's average sleep time over two consecutive days is no less than 7 hours, i.e., $x + y \geq 14$, and $(x, y)$ corresponds to the points on the sides and within the pentagon $EBCEF$, as shown in Figure 2.

Therefore, the probability of the desired event is
$$
1 - \frac{S_{\triangle AEF}}{S_{\text{square } ABCD}} = 1 - \frac{2}{9} = \frac{7}{9}.
$$