The times of five consecutive uniform intervals are 7:30 a.m., 9:50 a.m., 12:10 p.m., ?, and 4:50 p.m. What is the time for the fourth interval?

The time for the 1st interval is 7:30 a.m.
The time for the 2nd interval is 9:50 a.m.
To find the duration, subtract the 1st interval time from the 2nd interval time:
From 7:30 a.m. to 9:30 a.m. is 2 hours.
From 9:30 a.m. to 9:50 a.m. is 20 minutes.
So, the duration of one interval is 2 hours and 20 minutes.

Let's verify this with the 2nd and 3rd intervals:
From 9:50 a.m. to 12:10 p.m.
From 9:50 a.m. to 10:00 a.m. is 10 minutes.
From 10:00 a.m. to 12:00 p.m. is 2 hours.
From 12:00 p.m. to 12:10 p.m. is 10 minutes.
Total duration = 10 minutes + 2 hours + 10 minutes = 2 hours and 20 minutes.
The uniform interval is indeed 2 hours and 20 minutes.

The 3rd interval is at 12:10 p.m. To find the 4th interval, add the uniform duration (2 hours and 20 minutes) to the 3rd interval time.
Add 2 hours to 12:10 p.m.:
$12:10 \text{ p.m.} + 2 \text{ hours} = 2:10 \text{ p.m.}$
Now, add 20 minutes to 2:10 p.m.:
$2:10 \text{ p.m.} + 20 \text{ minutes} = 2:30 \text{ p.m.}$

The 5th interval is at 4:50 p.m. If our 4th interval time (2:30 p.m.) is correct, adding 2 hours and 20 minutes to it should give 4:50 p.m.
Add 2 hours to 2:30 p.m.:
$2:30 \text{ p.m.} + 2 \text{ hours} = 4:30 \text{ p.m.}$
Add 20 minutes to 4:30 p.m.:
$4:30 \text{ p.m.} + 20 \text{ minutes} = 4:50 \text{ p.m.}$
This matches the given 5th interval time, confirming our calculation.

The nurse will check on the patient in the 4th interval at $\boxed{\text{2:30 p.m.}}$.