Objects such as asteroids and comets that come into proximity with the Earth are called near-Earth objects (NEOs). The National Aeronautics and Space Administration (NASA) tracks and catalogs all NEOs that are at least 1 kilometer wide. Data on NEOs can be found on the NASA website. The following table gives the relative velocities in kilometers per second (km/s), arranged in increasing order, for the NEO close approaches to the earth during June 2013. 

The sample mean and sample standard deviation of these velocities are 11.9 km/s and 6.5 km/s, respectively. Modeling your solutions after those in Example 3.15.

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

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

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