
Dal J. answered 11/18/14
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That depends on what your first statement means. Does it mean that 85% of all new cancer cases were caused by smoking? Then multiply .85 times 186,516.
Or, does it mean that, among smokers, 85% of the cancer cases were caused by smoking? Then you can't answer the question, because the 186K number isn't broken out by smoker/nonsmoker.
Googling, the 85% seems to be of lung cancer deaths, rather than lung cancer cases, but it's not too far out of line to assume that cases are roughly proportional to deaths.