We must emphasize, eating bananas, working as airline flight crew or living in locations with, increases your annual dose rate. But it does not mean, that it must be dangerous. In each case, intensity of radiation also matters. It is very similar as for heat from a fire (less energetic radiation). If you are too close, the intensity of heat radiation is high and you can get burned. If you are at the right distance, you can withstand there without any problems and moreover it is comfortable. If you are too far from heat source, the insufficiency of heat can also hurt you. This analogy, in a certain sense, can be applied to radiation also from radiation sources.
In case of internal radiation, we are talking usually about so called “low doses”. Low dose here means additional small doses comparable to the normal background radiation (10 µSv = average daily dose received from natural background). The doses are very very low and therefore the probability of cancer induction could be almost negligible. Secondly, and this is crucial, the truth about low-dose radiation health effects still needs to be found. It is not exactly known, whether these low doses of radiation are detrimental or beneficial (and where is the threshold). Government and regulatory bodies assume a LNT model instead of a threshold or hormesis not because it is the more scientifically convincing, but because it is the more conservative estimate. Problem of this model is that it neglects a number of defence biological processes that may be crucial at low doses. The research during the last two decades is very interesting and show that small doses of radiation given at a low dose rate stimulate the defense mechanisms. Therefore the LNT model is not universally accepted with some proposing an adaptive dose–response relationship where low doses are protective and high doses are detrimental. Many studies have contradicted the LNT model and many of these have shown adaptive response to low dose radiation resulting in reduced mutations and cancers. This phenomenon is known as radiation hormesis.