On the average, how long do patients live when they have been diagnosed as being in the "end stage" of Alzheimers?

Because most people don't actually die of the Alzheimers, I don't think there is any meaningful average. Sorry.

Most ALs are not able to properly take care of any kind of advanced disease be it dementia or something else, that is why there are nursing homes. Since Alz is a very lengthy disease and even "end stage" may last years it can be difficult to pinpoint when someone has reached the final months, but she qualified for hospice so someone must have felt that she fit the criteria. Would you care to share any more details?

About all I can tell you is that she started acting strange last year, about mid-July...my aunt was visiting. My Mom stuck a couple of ragged pieces of toilet paper into her ears and came to the dinner table. I asked her why... she has been hard of hearing for several years so I speak louder when talking to her. She shrieked at me with some incomprehensible reply and my aunt asked, "What's the matter with you?!" So she has had mental aberrations for well over a year...I don't know how long the "end stage" would last.

I checked your profile and see that you have been active on the forum for a while now - have you never looked up the stages of Alzheimer's?
https://www.agingcare.com/articles/stages-of-alzheimers-disease-118964.htm

People don't usually go from diagnosis to end stage in under a year, in fact 5 - 10 years or more is the norm. I don't know what is going on with your mother but it sounds very confusing.