When using Chebyshev's Theorem,the minimum percentage of sample observations that will fall within two standard deviations of the mean will be ________ the percentage within two standard deviations if a normal distribution is assumed (Empirical Rule).
A)smaller than
B)greater than
C)the same as

Question

Quizplus · Accepted Answer

Chebyshev's theorem is a general rule that applies to all types of probability distributions, including skewed distributions. It states that regardless of the shape of the distribution, at least 75% of the data observations will fall within two standard deviations of the mean, and at least 89% of the data observations will fall within three standard deviations of the mean. Thus, the minimum percentage of sample observations that will fall within two standard deviations of the mean using Chebyshev's Theorem is smaller than the percentage within two standard deviations if a normal distribution is assumed (Empirical Rule). The Empirical Rule states that for a normal distribution, approximately 68% of the data observations will fall within one standard deviation of the mean, approximately 95% will fall within two standard deviations of the mean, and approximately 99.7% will fall within three standard deviations of the mean.

When Using Chebyshev's Theorem,the Minimum Percentage of Sample Observations That