Final answer:
The Springfield Meteorological Center's forecast is very accurate if it rained on 65% to 74% of the days predicted to have a 70% chance of rain. Probabilities cannot exceed 100%, so it's wrong to add the percentages for rain over two days. Lastly, a home run's probability is part of the overall chance of getting a hit, not greater than it.
Step-by-step explanation:
The correct response to the Springfield Meteorological Center's forecast question is that a 70% chance of rain forecast can be considered very accurate if it rained on 65% to 74% of those days (Option D). This range is closest to the predicted 70%, and in the context of weather forecasting, this would generally be accepted as a good match between the forecast and the actual outcome. A higher or lower range would indicate less accuracy in the prediction.
Explanation of Incorrect Statements About Probability :
In response to a statement (a), probabilities cannot exceed 100%, so adding the chance of rain for two separate days incorrectly assumes independence and compounds the probabilities. The actual combined probability would have to be recalculated taking into account the possibility of rain on both days or either day, without exceeding 100%.
As for statement (b), the probability that a baseball player hits a home run is a subset of the probability of getting any hit, so it cannot be greater. This is because all home runs count as hits, but not all hits are home runs.
Statistical Analysis:
In the case of the summer rainfall study, we'd perform a hypothesis test using the given mean, standard deviation, and alpha levels to determine if the observed mean rainfall is significantly different from the reported average.