According to the Statistical Summary of Students and Staff, prepared by the Department of Information Resources and Communications, Office of the President, University of California, the Fall 2012 enrollment figures for undergraduates at the University of California campuses were as follows.

Campus Enrollment (1000s)

Berkeley ................25.8

Davis ....................25.8

Irvine ......................22.1

Los Angeles ..............27.7

Merced .................... 5.4

Riverside ................18.6

San Diego ...............22.7

Santa Barbara ..........19.0

Santa Cruz ..............16.0

a. Compute the population mean enrollment, μ, of the UC campuses.

b. Compute σ. (Round your answer to two decimal places.)

c. Letting x denote enrollment, specify the standardized variable, z, corresponding to x.

d. Without performing any calculations, give the mean and standard deviation of z. Explain your answers.

e. Construct dotplots for the distributions of both x and z. Interpret your graphs.

f. Obtain and interpret the z-scores for the enrollments at the Los Angeles and Riverside campuses.