why is the half life 80s ? is this question wrong?

There is no problem with the question, only that the answer is wrong.

The half-life should be read on the graph for a count-rate of 75, i.e. about 46 s.

(An additional point to note, for answer to part (c), indoor radon is not a significant background source as far as external irradiation is concerned because radon is an alpha emitter. I would prefer to give "natural radionuclides in building material" as the answer. These radionuclides include uranium and radium, which are strong gamma emitters)