1992 DeVille running bad

Hi everyone. It's been a while. Everything is good with my vehicles. However, my uncle has a 1992 DeVille that is running very rough. It is sputtering and missing real bad. This condition came on all of a sudden.  It had all new plugs, new wires and filters done a year ago. He has only put on about 2,000 miles on it since the work was done.  It has been diagnosed by an auto electric shop as having 3 bad fuel injectors.  It is the same shop that did the tune up.  They want $800 for three injectors or $1500 for all eight.  I have never had a car with bad injectors so my knowledge on the subject is nill.  I guess common sense would tell me that the diagnosis could be correct.  What do any of you think.  Also, how does the repair price sound.   Thanks as usual.
 
Eddiek

Well, i know they can go bad.
I had a couple replaced on my 95 chevy lumina.
The car ran terrible before getting them replaced.
 
I can't recall the price, but it wasn't
a cheap fix.

the vast majority of "bad injectors" is actually the connection.
what was done to make that diag?

were the connectors taken off the injectors, cleaned,  dielectric greased, and reinserted?

Thanks for the replies. It's my uncle's car, so I'm not sure how they came up with the diagnosis.  I asked how they knew that the injectors were bad and all he told me was that they said three were shot and that he should have all 8 replaced.  My brothers 1995 Camaro had the exact same symtoms.  Ran great after they were replaced.  My uncle had a bad habit of running regular fuel instead of premium in that car.  Maybe that helped create the problem.   I told him that was a no no for a 1992 Cadillac. 
 
Eddiek