Final answer:
According to the Empirical Rule, 68% of values lie within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99.7% within 3 standard deviations. Chebyshev's Rule indicates at least 95% within 4.5 standard deviations, suggesting more than 95% within 4 standard deviations.
Step-by-step explanation:
The question deals with the Empirical Rule which is a statistical rule stating the percentage of values that lie within certain standard deviations from the mean in a normal distribution. For a normal distribution with a mean (μ) of 11 and a standard deviation (σ) of 2:
- 68% of the values lie within 1 standard deviation of the mean (μ ± σ).
- 95% of the values lie within 2 standard deviations of the mean (μ ± 2σ).
- 99.7% of the values lie within 3 standard deviations of the mean (μ ± 3σ).
For 4 standard deviations from the mean (μ ± 4σ), Chebyshev's Rule states that at least 95% of the data is within 4.5 standard deviations of the mean; therefore, it can be assumed that a slightly higher percentage falls within 4 standard deviations, although the exact percentage is not specified by the Empirical Rule