Can you teach a tone deaf child to sing?

[SarfEast1cated]

This is possibly not the right place for this question, but I'm not sure where else to put it.
So, my DD is 8, she loves singing, but isn't very good at it! She sings really flat (as do I and my mother too - I blame myself). Is it possible to teach her how to sing in tune? She loves it so much, I'd happily pay for lessons, so she gets picked for the choir.
Any suggestions?

I got 35/36 on that test. Means I cannot be called tone deaf.

The sound coming out of my mouth... sounds fine to me. I think it matches the sound I am suppose to make reasonably well. But I'm told I sound awful. Not just missing the correct sound, but not even in the same key. That key thing is obvious to other people. I can study keys in theory and I can even tell the odd one out if it's only one note while practising scales.

So not trusting the lab test, because I still fail the practical!!

I'm not at all knowledgeable on the subject, but I've heard something which seems true in my limited experience: it's tremendously helpful to hear songs sung unaccompanied at a pitch which is comfortable for you, and to hear them repeated often. I guess where most people who sing quite badly struggle is that they haven't developed a good enough ear.

Around the age of six, my younger daughter showed no interest in singing and rarely tried. What she did sing was usually not tuneful. She happened to be a fan of a very good tape featuring nursery rhymes sung by young choristers. Eventually she began to come out with those same nursery rhymes herself quite beautifully, without practice. She still isn't too interested, but the potential is clear.

My teenager is quite a decent singer, and practises around the house, so the family hear specific songs repeated a lot. My younger daughter and I can now sing those songs reasonably well. We're much better at picking up other songs than we once were.

Have you ever noticed how badly most people sing "Happy Birthday"? My theory is that we hear it sung badly quite often, which means that few people really know it properly. Most of us have little opportunity to hear it sung well repeatedly. I am extremely shaky on that one!