check engine ant ETS light = bad EGR valve

My new to me '97 Skylark custom 2.4 with 68,000 miles
had its check engine and ETS light just came on this week at the same time is that normal?
the mechanic says it is a
code p0404 EGR feedback signal out of range.
and p0304.cyl. 4 misfire detected
and tells me to repkace the EGR at $360.00
Both lights were on and off from time to time earlier this week but now both are on at start up by the way.the car seems to run smooth at least for now.

Is it normal for the traction control light and check engine to come on at the same
time?
..Does anyone have any tips to deal with the EGR short of replacement. Thank you for your time.

Welcome to AF. Don't know how your tech determined the egr had failed, could be another issue such as blocked passages, or controls. Traction control could be another issue that rerquires ebcm capability to scan, it is also possible the etc is disabled if the pcm sees the misfire code, addt'l diagnosis is required here. Your tech really should be capable of dealing with these questions if you are contracting with him to do repairs, if replaces the egr and the problem comes back, make sure he understands you want some sort of assurance that is the problem with that code.

Sorry I should of mentioned that it does say "Diagnose bad EGR valve-{and what seems to be the word laser} what ever it cost 37 dollars. plus $29 for the code readings. . I only add this in case it means anything to you..Thanks for the input!

It most likely is an EGR valve causing the problem.It's a common problem with GM vehicles.That would not cause the #4 misfire that you have.I would recommend having the injectors professionally cleaned.The crap that goes in the tank usually doesn't help.Good luck!