Question

the weights of 2-pound bags of best dog food are approximately normally distributed with a given mean μ and standard deviation σ. according to the empirical rule, what percentage of the bags will have weights within 3 standard deviations of the mean?
○ 47.5%
○ 68%
○ 95%
○ 99.7%

Explanation:

Step1: Recall Empirical Rule

The Empirical Rule (or 68 - 95 - 99.7 rule) for normal distributions states:

• Approximately 68% of data lies within \(1\) standard deviation (\(\sigma\)) of the mean (\(\mu\)).
• Approximately 95% of data lies within \(2\) standard deviations of the mean.
• Approximately 99.7% of data lies within \(3\) standard deviations of the mean.

Step2: Apply to the Problem

The question asks for the percentage of bags with weights within \(3\) standard deviations of the mean. Using the Empirical Rule, this percentage is approximately 99.7%.

Answer:

99.7% (corresponding to the option with 99.7%, likely the last option in the given choices)