Question

Which of the following can be used to determine the proportion of data points that fall within a specified number of standard deviations from the mean?multiple select question.

a. chebyshev's theoremper
b. centilesthe empirical rule - assuming
c. a normal distribution the mode

Answer 1

Chebyshev's theorem and the empirical rule can be used to determine the proportion of data points within a specified number of standard deviations from the mean for different types of distributions. The correct options are (a) and (b).

Step-by-step explanation:

The correct options that can be used to determine the proportion of data points that fall within a specified number of standard deviations from the mean are:

• Chebyshev's theorem: Chebyshev's theorem states that regardless of the shape of the distribution, at least 75% of the data falls within two standard deviations of the mean, at least 89% of the data falls within three standard deviations, and at least 95% of the data falls within 4.5 standard deviations from the mean.

• The empirical rule: This rule applies specifically to bell-shaped and symmetric distributions. It states that approximately 68% of the data falls within one standard deviation, 95% of the data falls within two standard deviations, and more than 99% of the data falls within three standard deviations of the mean.