Question

the weights of 2-pound bags of best dog food are approximately normally distributed with a given mean \\(\mu\\) and standard deviation \\(\sigma\\). 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:

State the Empirical Rule percentages

Using the Empirical Rule knowledge point

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

Identify the target percentage

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

Answer:

• (A) 47.5%
• (B) 68%
• (C) 95%
• (D) 99.7% (Correct answer)