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Each February the groundhog checks his shadow to see how much longer winter will last. In each of these independent events there is a 50% chance that the groundhog correctly predicts the end of winter (50% that he is incorrect). Since the early 1970s, the groundhog has predicted a longer winter 16 out of 30 times.
A. What is the probability that the groundhog will make at least 16 correct predictions in 30 years?
B. A meteorologist, using weather patterns, can predict correctly the end of winter with a probability of more than 50%. Given that the meteorologist makes predictions over the next 30 years, would we expect to see more variability in the outcomes of the groundhog or the meteorologist? Explain.
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