Speed of light from galaxies. Refer to The Astronomical Journal study of galaxy velocities...

Speed of light from galaxies. Refer to The Astronomical Journal study of galaxy velocities, presented in Exercise. A second cluster of galaxies, named A1775, is thought to be a double cluster —that is, two clusters of galaxies in close proximity. Fifty-one velocity observations (in kilometers per second, km/s) from cluster A1775 are listed in the table. The data are saved in the GALAXY2 file.

Based on Oegerle, W. R., Hill, J. M., and Fitchett, M. J. “Observations of high dispersion clusters of galaxies: Constraints on cold dark matter.” The Astronomical Journal, Vol. 110, No. 1, July 1995 (Table and Figure).

a. Use a graphical method to describe the velocity distribution of galaxy cluster A1775.

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b. Examine the graph you created in part a. Is there evidence to support the double-cluster theory? Explain.

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c. Calculate numerical descriptive measures (e.g., mean and standard deviation) for galaxy velocities in cluster A1775. Depending on your answer to part b, you may need to calculate two sets of numerical descriptive measures, one for each of the clusters (say, A1775A and A1775B) within the double cluster.

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d. Suppose you observe a galaxy velocity of 20,000 km/s. Is this galaxy likely to belong to cluster A1775A or A1775B? Explain.

Speed of light from galaxies. 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.

Source: Oegerle, W. R., Hill, J. M., and Fitchett, M. J. “Observations of high dispersion clusters of galaxies: Constraints on cold dark matter.” The Astronomical Journal, Vol. 110, No. 1, July 1995, p. 37. Reproduced by permission of the AAS.

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.

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b. The mean and standard deviation of the 103 velocities observed in galaxy cluster A2142 were reported as  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.

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c. Recommend a single velocity value to be used in the CDM model for galaxy cluster A2142. Explain your reasoning.

Best-paid CEOs. Forbes magazine conducts an annual survey of the salaries of chief executive officers. In addition to salary information, Forbes collects and reports personal data on the CEOs, including their level of education and age. Do most CEOs have advanced degrees, such as master’s degrees or doctorates? The data in the accompanying table (saved in the FORBES40 file) represent the highest degree earned by each of the top 40 best-paid CEOs of 2010. Use a graphical method to summarize the highest degree earned by these CEOs. What is your opinion about whether most CEOs have advanced degrees?

Based on “40 highest-paid CEOs of 2010” from “What the boss makes: CEO compensation.” Forbes, April 28, 2010.