Astronomers theorize that cold dark matter caused the formation of galaxies and clusters of galaxies in the universe. The theoretical model for cold dark matter requires an estimate of the velocities of light emitted from galaxy clusters. The Astronomical Journal (July 1995) published a study of observed velocities of galaxies in four different clusters. Galaxy velocity was measured in kilometers per second (km/s), using a spectrograph and high-power telescope.
a. The observed velocities of 103 galaxies located in the cluster named A2142 are summarized in the accompanying histogram. Comment on whether the empirical rule is applicable to describing the velocity distribution for this cluster.
b. The mean and standard deviation of the 103 velocities observed in galaxy cluster A2142 were reported as x-bar = 27,117 km/s and s = 1,280 km/s, respectively. Use this information to construct an interval that captures approximately 95% of the velocities of the galaxies in the cluster.
c. Recommend a single velocity value to be used in the CDM model for galaxy cluster A2142. Explain your reasoning.

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