According to a recent report, scientists in New England say they have identified a set of genetic variants that predicts extreme longevity with 77% accuracy (New York Times, July 1, 2010). Assume 150 patients decide to get their genome sequenced.
a. If the claim by scientists is accurate, what is the probability that more than 120 patients will get a correct diagnosis for extreme longevity?
b. If the claim by scientists is accurate, what is the probability that fewer than 70% of the patients will get a correct diagnosis for extreme longevity?