(Or, with no calculation: The thing about a Poisson distribution is that it's what you get from a memoryless process. If the bulb almost always burns out within, say, a week of reaching 1 month, then it should also almost always burn out within a week of first being switched on. So its mean lifetime can't be much longer than the typical variation.)

It sounds to me more as if lifetime was proportional to some physical characteristic(s) of the bulb that were controlled in the manufacturing process. For instance, maybe lifetime was proportional to thickness of filament or something of the sort. (In which case, the vendors could have made the bulbs last longer, but perhaps only by also making them more expensive. Though it's tempting to speculate that they were designed not to last too long, so that you had to buy more.)