Use the table to find the area under the standard normal curve and above the interval $[-0.77, \infty)$ on the horizontal axis. The area is (Type an integer or decimal rounded to four decimal places as needed.)

Step 1 ：The area under the standard normal curve represents the probability of an event occurring. The total area under the curve is 1. The area above the interval $[-0.77, \infty)$ is equivalent to the area from $[-\infty, 0.77]$. We can find this area by looking up the z-score of 0.77 in a standard normal distribution table.

Step 2 ：The area under the standard normal curve and above the interval $[-0.77, \infty)$ on the horizontal axis is calculated to be approximately 0.7793500536573503.

Step 3 ：Rounding to four decimal places, the final answer is \(\boxed{0.7794}\).