Population. The Census of India provides a variety of statistical information on different aspects of the Indian population. According to the Population Enumeration Data for the 2011 census, provided on the official website for the Indian census censusindia.gov.in, the top 9 metro cities on the basis of their population are as follows.

City Population (in million)

Mumbai 18.4 Delhi 16.3 Kolkatta 14.1 Chennai 8.7 Bangalore 8.5 Hyderabad 7.8 Ahemdabad 6.4 Pune 5.1 Surat 4.6

a. Compute the population mean enrolment, μ, of the cities. (Round your answer to two decimal places.)

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

c. Letting x denote a city, 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 Mumbai and Bangalore.