Every year on Groundhog Day (February 2), the famous groundhog Punxsutawney Phil tries to predict whether there

Question:

Every year on Groundhog Day (February 2), the famous groundhog Punxsutawney Phil tries to predict whether there will be 6 more weeks of winter. The article “Groundhog Has Been Off Target” (USA Today, Feb. 1, 2011) states that “based on weather data, there is no predictive skill for the groundhog.” Suppose that you plan to take a random sample of 20 years and use weather data to determine the proportion of these years the groundhog’s prediction was correct.
a. Describe the shape, center, and spread of the sampling of for samples of size 20 if the groundhog has only a 50–50 chance of making a correct prediction.
b. Based on your answer to Part (a), what sample proportion values would convince you that the groundhog’s predictions have a better than 50–50 chance of being correct? Distribution
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