Objects such as asteroids and comets that come into proximity with the Earth are callednear-Earth objects(NEOs). The National Aeronautics and Space Administration(NASA) tracks and catalogues all NEOs that are at least 1 kilometer wide. Data on NEOs can be found on the NASA website. The accompanying table gives the relative velocities in kilometers per second(km/s), arranged in increasingorder, for some of the NEO close approaches to the Earth during June 2013. The sample mean and sample standard deviation of these velocities are 12.2 km/s and 6.6 km/s, respectively. Complete parts(a) through(c) below.

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a. Compare the percentage of the observations that actually lie within two standard deviations to either side of the mean with that given byChebyshev's rule with k=2.

The percentage of observations that actually lie within two standard deviations to either side of the mean is = %

Chebyshev's rule states that when k=2, at least = % of the observations in any data set lies within two standard deviations to either side of the mean.

b. Repeat part(a) with k=3.

The percentage of observations that actually lie within three standard deviations to either side of the mean is = %

Chebyshev's rule states that when k=3, at least = % of the observations in any data set lies within three standard deviations to either side of the mean.

c. Interpret your results from parts(a) and(b).

A.

Chebyshev's rule gives only an average for the percentage of observations that lie within a specified number of standard deviations to either side of themean; the actual percentage will usually be higher.

B.

Chebyshev's rule gives a minimum for the percentage of observations that lie within a specified number of standard deviations to either side of themean; the actual percentage will usually be the same.

C.

Chebyshev's rule gives only a minimum for the percentage of observations that lie within a specified number of standard deviations to either side of themean; the actual percentage will usually be higher.

D.

Chebyshev's rule gives only a maximum for the percentage of observations that lie within a specified number of standard deviations to either side of themean; the actual percentage will usually be lower.