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Answer :
Final Answer:
According to the 68-95-99.7 Rule, approximately 68% of the bags will have proportions within one standard deviation of the mean, about 95% will fall within two standard deviations, and roughly 99.7% will lie within three standard deviations. Therefore, option B) 68% and 99.7% represents the correct range of proportions.
Explanation:
The 68-95-99.7 Rule, also known as the empirical rule, states that for a normal distribution:
- About 68% of the data falls within one standard deviation of the mean.
- Approximately 95% of the data falls within two standard deviations of the mean.
- Roughly 99.7% of the data falls within three standard deviations of the mean.
In the context of the question, which asks about the variation in proportion from bag to bag, we can apply this rule to understand the distribution of proportions across multiple bags. For example, if the proportion of a certain item in one bag follows a normal distribution, then approximately 68% of bags will have proportions within one standard deviation of the mean proportion.
Based on this understanding, we can deduce that the percentage of bags with proportions between 68% and 99.7% represents the range where the vast majority of bags' proportions will fall. Therefore, option B) 68% and 99.7% accurately captures the variation in proportions across bags according to the 68-95-99.7 Rule.
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